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What is the Least Common Multiple of 69360 and 69380?

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 69360 and 69380 is 240609840.

LCM(69360,69380) = 240609840

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Least Common Multiple of 69360 and 69380 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69360 and 69380, than apply into the LCM equation.

GCF(69360,69380) = 20
LCM(69360,69380) = ( 69360 × 69380) / 20
LCM(69360,69380) = 4812196800 / 20
LCM(69360,69380) = 240609840

Least Common Multiple (LCM) of 69360 and 69380 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69360 and 69380. First we will calculate the prime factors of 69360 and 69380.

Prime Factorization of 69360

Prime factors of 69360 are 2, 3, 5, 17. Prime factorization of 69360 in exponential form is:

69360 = 24 × 31 × 51 × 172

Prime Factorization of 69380

Prime factors of 69380 are 2, 5, 3469. Prime factorization of 69380 in exponential form is:

69380 = 22 × 51 × 34691

Now multiplying the highest exponent prime factors to calculate the LCM of 69360 and 69380.

LCM(69360,69380) = 24 × 31 × 51 × 172 × 34691
LCM(69360,69380) = 240609840