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What is the Least Common Multiple of 67977 and 67992?

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 67977 and 67992 is 1540630728.

LCM(67977,67992) = 1540630728

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Least Common Multiple of 67977 and 67992 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67977 and 67992, than apply into the LCM equation.

GCF(67977,67992) = 3
LCM(67977,67992) = ( 67977 × 67992) / 3
LCM(67977,67992) = 4621892184 / 3
LCM(67977,67992) = 1540630728

Least Common Multiple (LCM) of 67977 and 67992 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67977 and 67992. First we will calculate the prime factors of 67977 and 67992.

Prime Factorization of 67977

Prime factors of 67977 are 3, 7, 13, 83. Prime factorization of 67977 in exponential form is:

67977 = 32 × 71 × 131 × 831

Prime Factorization of 67992

Prime factors of 67992 are 2, 3, 2833. Prime factorization of 67992 in exponential form is:

67992 = 23 × 31 × 28331

Now multiplying the highest exponent prime factors to calculate the LCM of 67977 and 67992.

LCM(67977,67992) = 32 × 71 × 131 × 831 × 23 × 28331
LCM(67977,67992) = 1540630728