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What is the Least Common Multiple of 67965 and 67972?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 67965 and 67972 is 4619716980.

LCM(67965,67972) = 4619716980

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Least Common Multiple of 67965 and 67972 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67965 and 67972, than apply into the LCM equation.

GCF(67965,67972) = 1
LCM(67965,67972) = ( 67965 × 67972) / 1
LCM(67965,67972) = 4619716980 / 1
LCM(67965,67972) = 4619716980

Least Common Multiple (LCM) of 67965 and 67972 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67965 and 67972. First we will calculate the prime factors of 67965 and 67972.

Prime Factorization of 67965

Prime factors of 67965 are 3, 5, 23, 197. Prime factorization of 67965 in exponential form is:

67965 = 31 × 51 × 231 × 1971

Prime Factorization of 67972

Prime factors of 67972 are 2, 16993. Prime factorization of 67972 in exponential form is:

67972 = 22 × 169931

Now multiplying the highest exponent prime factors to calculate the LCM of 67965 and 67972.

LCM(67965,67972) = 31 × 51 × 231 × 1971 × 22 × 169931
LCM(67965,67972) = 4619716980