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.

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