0
The least common multiple of two or more nonzero whole numbers is the smallest whole number that is divisible by each of the numbers. There are two common methods for finding the least common multiple of 2 numbers.
Method 1:
List the multiples of each number, and look for the smallest number that appears in each list.
Example:
Find the least common multiple of 12 and 42. We list the multiples of each number:
12: 12, 24, 36, 48, 60, 72, 84, ...
42: 42, 84, 126, 168, 190, ...
We see that the number 84 is the smallest number that appears in each list.
Method 2:
Factor each of the numbers into primes. For each different Prime number in either of the factorizations, follow these steps:
1. Count the number of times it appears in each of the factorizations.
2. Take the largest of these two counts.
3. Write down that prime number as many times as the count in step 2.
To find the least common multiple take the product of all of the prime numbers written down in steps 1, 2, and 3.
Example:
Find the least common multiple of 24 and 90. First, we find the prime factorization of each number.
24 = 2 × 2 × 2 × 3
90 = 2 × 3 × 3 × 5
The prime numbers 2, 3, and 5 appear in the factorizations. We follow steps 1 through 3 for each of these primes.
The number 2 occurs 3 times in the first factorization and 1 time in the second, so we will use three 2's.
The number 3 occurs 1 time in the first factorization and 2 times in the second, so we will use two 3's.
The number 5 occurs 0 times in the first factorization and 1 time in the second factorization, so we will use one 5.
The least common multiple is the product of three 2's, two 3's, and one 5.
2 × 2 × 2 × 3 × 3 × 5 = 360
Example:
Find the least common multiple of 14 and 49. First, we find the prime factorization of each number.
14 = 2 × 7
49 = 7 × 7
The prime numbers 2 and 7 appear in the factorizations. We follow steps 1 through 3 for each of these primes.
The number 2 occurs 1 times in the first factorization and 0 times in the second, so we will use one 2.
The number 7 occurs 1 time in the first factorization and 2 times in the second, so we will use two 7's.
The least common multiple is the product of one 2 and two 7's.
2 × 7 × 7 = 98
Examples:
Some other least common multiples are listed below.
The least common multiple of 12 and 9 is 36.
The least common multiple of 6 and 18 is 18.
The least common multiple of 2, 3, 4, and 5 is 60.
450 is not the LCM of 17 and 23.
689 is not the LCM of 15 and 20.
This is much easier than the other way.
Predict
Add your answer:
Earn +20 pts
What is the least common multiple of 14 and 27?
The least common multiple of 14 and 27 is 378
What is the least common multiple of 13 and 35?
The least common multiple of 35 , 13 = 455The least common multiple of 35 , 13 = 455
What is the least common multiple of 9 and 34?
The least common multiple of 6 and 34 is 102.
What is the least common multiple of 78?
There is not a least common multiple of a single number, such as 78, because there cannot be a least common multiple without two or more numbers to compare. Common multiples are multiples that the numbers being compared have in common. The least common multiple is the smallest multiple that all the numbers being compared have in common. Examples: The least common multiple of 18 and 78 is 234. The least common multiple of 52 and 78 is 156. The least common multiple of 78 and 195 is 390.
The least number that is a common multiple is called what?
The least common multiple, or LCM.
The least number that a common multiple is called?
That's known as the least common multiple, or LCM.
Is the least common multiple of the denominators?
The least common denominator is the least common multiple of the denominators.
What is the least common multiple of 14 and 27?
The least common multiple of 14 and 27 is 378
The least number that is a common multiple is called the?
least common multiple
What is the least common multiple of 18 and 56?
The least common multiple of 18 , 56 = 504
What is the least common multiple of 15 and 38?
The Least Common Multiple (LCM) for 38 15 is 570.
What is the least common multiple of 29 and 30?
Least common multiple of 29 and 30 is 870.
What is the least common multiple of 13 and 35?
The least common multiple of 35 , 13 = 455The least common multiple of 35 , 13 = 455
What is the least common multiple of 9 and 34?
The least common multiple of 6 and 34 is 102.
What is the least common multiple of 36?
There is not a least common multiple of a single number, such as 36, because there cannot be a least common multiple without two or more numbers to compare. Common multiples are multiples that the numbers being compared have in common. The least common multiple is the smallest multiple that all the numbers being compared have in common. Examples: The least common multiple of 27 and 36 is 108. The least common multiple of 32 and 36 is 288. The least common multiple of 36 and 72 is 72.
What is the least common multiple of 49?
There is not a least common multiple of a single number, such as 49, because there cannot be a least common multiple without two or more numbers to compare. Common multiples are multiples that the numbers being compared have in common. The least common multiple is the smallest multiple that all the numbers being compared have in common. Examples: The least common multiple of 3 and 49 is 147. The least common multiple of 14 and 49 is 98. The least common multiple of 49 and 196 is 196.
What is the least common multiple of 7810?
There is not a least common multiple of a single number, such as 7810, because there cannot be a least common multiple without two or more numbers to compare. Common multiples are multiples that the numbers being compared have in common. The least common multiple is the smallest multiple that all the numbers being compared have in common. Examples: The least common multiple of 3 and 7810 is 23,430. The least common multiple of 220 and 7810 is 15,620. The least common multiple of 355 and 7810 is 7810.
