# Find three pairs of numbers for which the least common multiple equals the product of the two numbers. We are asked to find three examples of pairs of numbers whose least common multiple is the product of the two numbers.

For any pair of positive integers that have a greatest common factor of 1, the least common multiple will be the product of the two numbers.

If gcd(a,b)=1...

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We are asked to find three examples of pairs of numbers whose least common multiple is the product of the two numbers.

For any pair of positive integers that have a greatest common factor of 1, the least common multiple will be the product of the two numbers.

If gcd(a,b)=1 then lcm(a,b)=ab

Ex: The least common multiple of (2,3) is 6. Multiples of 2 are 2,4,6,8,... while multiples of 3 are 3,6,9,... and it can be seen that the least common multiple is 6.

Ex: (3,5) the least common multiple is 15.

Ex: (5,11) The least common multiple is 55.