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What is the Least Common Multiple of 360 and 380?

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 360 and 380 is 6840.

LCM(360,380) = 6840

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Least Common Multiple of 360 and 380 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 360 and 380, than apply into the LCM equation.

GCF(360,380) = 20
LCM(360,380) = ( 360 × 380) / 20
LCM(360,380) = 136800 / 20
LCM(360,380) = 6840

Least Common Multiple (LCM) of 360 and 380 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 360 and 380. First we will calculate the prime factors of 360 and 380.

Prime Factorization of 360

Prime factors of 360 are 2, 3, 5. Prime factorization of 360 in exponential form is:

360 = 23 × 32 × 51

Prime Factorization of 380

Prime factors of 380 are 2, 5, 19. Prime factorization of 380 in exponential form is:

380 = 22 × 51 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 360 and 380.

LCM(360,380) = 23 × 32 × 51 × 191
LCM(360,380) = 6840