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What is the Least Common Multiple of 1224 and 1230?

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 1224 and 1230 is 250920.

LCM(1224,1230) = 250920

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Least Common Multiple of 1224 and 1230 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1224 and 1230, than apply into the LCM equation.

GCF(1224,1230) = 6
LCM(1224,1230) = ( 1224 × 1230) / 6
LCM(1224,1230) = 1505520 / 6
LCM(1224,1230) = 250920

Least Common Multiple (LCM) of 1224 and 1230 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1224 and 1230. First we will calculate the prime factors of 1224 and 1230.

Prime Factorization of 1224

Prime factors of 1224 are 2, 3, 17. Prime factorization of 1224 in exponential form is:

1224 = 23 × 32 × 171

Prime Factorization of 1230

Prime factors of 1230 are 2, 3, 5, 41. Prime factorization of 1230 in exponential form is:

1230 = 21 × 31 × 51 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 1224 and 1230.

LCM(1224,1230) = 23 × 32 × 171 × 51 × 411
LCM(1224,1230) = 250920