when will the lcm of tow numbers be the product of the number.
when they have no factors in common.
LCM(a,b) = ab / GCF(a,b)
question
The least common multiple (LCM) of two numbers will be equal to the product of those two numbers only when the two numbers are co-prime or relatively prime, which means they have no common factors other than 1.
To find the LCM, follow these steps:
1. Start by factoring both numbers into their prime factors.
2. Take the highest power of each prime factor that appears in either number.
3. Multiply all these prime factors together.
For example, let's consider the numbers 4 and 9:
The prime factorization of 4 is 2 * 2.
The prime factorization of 9 is 3 * 3.
Taking the highest power of each prime factor, we have:
2 (which appears twice) * 3 (appearing twice) = 2^2 * 3^2 = 4 * 9 = 36.
So, the LCM of 4 and 9 is 36, which is not equal to their product because 4 and 9 are not co-prime.
In order for the LCM to be equal to the product of the two numbers, there should be no common prime factors between them. So, if the two numbers are prime or have no prime factors in common, then their LCM will be equal to their product.