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Short answer: Yes.
Long answer:
Explanation:
lcm means least common multiple,
gcd means greatest common divisor,
|a| means the absolute of a,
a / b means a divided by b,
a * b means a multiplied by b
Premise: Let a and b be a natural numbers, i.e. a ⋲ IN, b ⋲ IN.
1: It is known that lcm(a, b) = (|a| * |b|) / gcd(a, b)
2: Also the gcd of two numbers is at least 1, or in math: ∀ a ⋲ IN: gcd(a, b) >= 1.
3: From 1 and 2 we can conclude: lcm(a, b) = |a| * |b| / gcd(a, b) <= |a| * |b|
4: From 3 and the premise we can conclude (because ∀ a ⋲ IN: |a| = a): lcm(a, b) <= a * b
5: Now the product of two natural numbers (like a and b) is a natural number as well, or in math: ∀ a ⋲ IN, b ⋲ IN: a * b ⋲ IN
6: From 2 and 5 we can finally conclude, that: ∀ a ⋲ IN, b ⋲ IN ∃ c ⋲ IN: lcm(a, b) <= c
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Smallest number that is a multiple of two numbers?
The smallest number that is a multiple of two given numbers is called the least common multiple (LCM) of those two numbers. It can be found by taking the product of the two numbers and dividing it by their greatest common divisor (GCD).
What is the same as a least common multiple?
Lowest common multiple is the smallest whole number that is divisible by all the numbers. eg. the lowest common multiple of 70 and 14 is 14, the lowest common multiple of 2 and 3 is 6, or 7 and 8 is 56 etc. Normally found by multiplying the two numbers together, then seeing if there are any smaller than that
What is the LCM of 45 55 495?
LCM(Least Common Multiple) as the name suggests is the common multiple of two numbers. Thus, LCM of a single number cannot be found out.
What information does the least common multiple of two numbers provide in a problem?
When adding or subtracting fractions with different denominators the lowest common denominator is needed and is found by finding the lowest common multiple of the denominators.
How do you find the highest common multiple?
By multiplying the highest prime factors in exponential terms found in two or more numbers
Smallest number that is a multiple of two numbers?
The smallest number that is a multiple of two given numbers is called the least common multiple (LCM) of those two numbers. It can be found by taking the product of the two numbers and dividing it by their greatest common divisor (GCD).
What is the highest common multiple of 3 and 5?
The highest common multiple of two numbers is their least common multiple (LCM). The LCM of 3 and 5 is found by multiplying the two numbers and dividing by their greatest common divisor (GCD). In this case, the LCM of 3 and 5 is 15, as 3 * 5 / 1 = 15.
What is the LCM of 562?
You need at least two numbers to find an LCM.
How does reduce the LCM of 70?
LCM(Least Common Multiple) as the name suggests is the common multiple of two numbers. Thus, LCM of a single number cannot be found out.
What is the LCM of 2300?
You need at least two numbers to find an LCM.
What is the LCM of 3512?
LCM(Least Common Multiple) as the name suggests is the common multiple of two numbers. Thus, LCM of a single number cannot be found out.
What is the same as a least common multiple?
Lowest common multiple is the smallest whole number that is divisible by all the numbers. eg. the lowest common multiple of 70 and 14 is 14, the lowest common multiple of 2 and 3 is 6, or 7 and 8 is 56 etc. Normally found by multiplying the two numbers together, then seeing if there are any smaller than that
What is the HCF and the LCM of 175?
You need at least two numbers to find either of those.
What is the lcm of 74 and 20?
LCM(Least Common Multiple) as the name suggests is the common multiple of two numbers. Thus, LCM of a single number cannot be found out.
What is the LCM of 109 and 128?
LCM(Least Common Multiple) as the name suggests is the common multiple of two numbers. Thus, LCM of a single number cannot be found out.
What is the LCM of 45 55 495?
LCM(Least Common Multiple) as the name suggests is the common multiple of two numbers. Thus, LCM of a single number cannot be found out.
What information does the least common multiple of two numbers provide in a problem?
When adding or subtracting fractions with different denominators the lowest common denominator is needed and is found by finding the lowest common multiple of the denominators.
