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What is the Least Common Multiple of 234 and 252?

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 234 and 252 is 3276.

LCM(234,252) = 3276

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Least Common Multiple of 234 and 252 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 234 and 252, than apply into the LCM equation.

GCF(234,252) = 18
LCM(234,252) = ( 234 × 252) / 18
LCM(234,252) = 58968 / 18
LCM(234,252) = 3276

Least Common Multiple (LCM) of 234 and 252 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 234 and 252. First we will calculate the prime factors of 234 and 252.

Prime Factorization of 234

Prime factors of 234 are 2, 3, 13. Prime factorization of 234 in exponential form is:

234 = 21 × 32 × 131

Prime Factorization of 252

Prime factors of 252 are 2, 3, 7. Prime factorization of 252 in exponential form is:

252 = 22 × 32 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 234 and 252.

LCM(234,252) = 22 × 32 × 131 × 71
LCM(234,252) = 3276

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