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Q: How big can the LCM be for any pair of natural numbers?

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The LCM can be any positive integer.

The LCM must be the other number in the pair. For any pair of numbers X and Y, X*Y = GCF*LCM and the result follows if you put GCF = X (or Y).

That pair of numbers doesn't exist, as the least common factor of any pair of positive numbers is 1. The LCM of 3 and 6 is 6. The GCF of 6 and 12 is 6.

Absolutely !.. Any prime number only has itself and 1 as its factors.

The LCM of any three distinct prime numbers is their product.

Related questions

The LCM can be any positive integer.

What is the LCM of 40

The LCM must be the other number in the pair. For any pair of numbers X and Y, X*Y = GCF*LCM and the result follows if you put GCF = X (or Y).

Pick any two numbers. All pairs of numbers have an LCM.

Any pair of prime numbers. 5 and 7 11 and 13

That pair of numbers doesn't exist, as the least common factor of any pair of positive numbers is 1. The LCM of 3 and 6 is 6. The GCF of 6 and 12 is 6.

For this you will need a couple of helper algorithms. The first is the GCD (greatest common divisor) which is expressed as follows:procedure GCD (a, b) isinput: natural numbers a and bwhile ab doif a>blet a be a-belselet b be b-aend ifend whilereturn aThe second algorithm is the LCM (least common multiple) of two numbers:procedure LCM (a, b) isinput: natural numbers a and b return (a*b) / GCD (a, b)Now that you can calculate the GCD and LCM of any two natural numbers, you can calculate the LCM of any three natural numbers as follows:procedure LCM3 (a, b, c) isinput: natural numbers a, b and c return LCM (LCM (a, b), c)Note that the LCM of three numbers first calculates the LCM of two of those numbers (a and b) and then calculates the LCM of that result along with the third number (c). That is, if the three numbers were 8, 9 and 21, the LCM of 8 and 9 is 72 and the LCM of 72 and 21 is 504. Thus the LCM of 8, 9 and 21 is 504.

35 and 36 are coprime (any pair of consecutive numbers must be). So lcm(35, 36) = 35*36 = 1260.

Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.

Absolutely !.. Any prime number only has itself and 1 as its factors.

The LCM is not defined for any set of numbers that contains a zero.

For any two natural numbers a & b: Their LCM is b if b is the multiple of a. Here, 135 is the multiple of 27(27 x 5 = 135). Therefore, LCM of 27 & 135 = 135.

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