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What is the Least Common Multiple of 67530 and 67542?

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 67530 and 67542 is 760185210.

LCM(67530,67542) = 760185210

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Least Common Multiple of 67530 and 67542 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67530 and 67542, than apply into the LCM equation.

GCF(67530,67542) = 6
LCM(67530,67542) = ( 67530 × 67542) / 6
LCM(67530,67542) = 4561111260 / 6
LCM(67530,67542) = 760185210

Least Common Multiple (LCM) of 67530 and 67542 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67530 and 67542. First we will calculate the prime factors of 67530 and 67542.

Prime Factorization of 67530

Prime factors of 67530 are 2, 3, 5, 2251. Prime factorization of 67530 in exponential form is:

67530 = 21 × 31 × 51 × 22511

Prime Factorization of 67542

Prime factors of 67542 are 2, 3, 11257. Prime factorization of 67542 in exponential form is:

67542 = 21 × 31 × 112571

Now multiplying the highest exponent prime factors to calculate the LCM of 67530 and 67542.

LCM(67530,67542) = 21 × 31 × 51 × 22511 × 112571
LCM(67530,67542) = 760185210