The LCM is 198.
What is the lcm of 66 and 99?
There are two notable methods of computing the LCM (lowest common multiple) between two numbers:
1. The unique prime factorization method states that any integer greater than one can be expressed as a product of its prime factors. The LCM will be the product of multiplying the highest power in each prime factor category together. Rendering back to your question:
66 = 2 * 33
99 = 3 * 33
LCM = 2 * 3 * 33 = 198
2. The following formula reduces the problem of computing the least common multiple to the problem of computing the greatest common divisor (GCD):
LCM (a, b) = |a * b| / GCD(a, b)
LCM (66, 99) = 66 * 99 / GCD(66, 99)
LCM (66, 99) = 66 * 99 / LCM (66, 99) = 6534 / 33 = 198
There are fast algorithms for computing the GCD that do not require the numbers to be factored, such as the Euclidean algorithm.
1. The unique prime factorization method states that any integer greater than one can be expressed as a product of its prime factors. The LCM will be the product of multiplying the highest power in each prime factor category together. Rendering back to your question:
66 = 2 * 33
99 = 3 * 33
LCM = 2 * 3 * 33 = 198
2. The following formula reduces the problem of computing the least common multiple to the problem of computing the greatest common divisor (GCD):
LCM (a, b) = |a * b| / GCD(a, b)
LCM (66, 99) = 66 * 99 / GCD(66, 99)
LCM (66, 99) = 66 * 99 / LCM (66, 99) = 6534 / 33 = 198
There are fast algorithms for computing the GCD that do not require the numbers to be factored, such as the Euclidean algorithm.
