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What is the Least Common Multiple of 1206 and 1214?

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 1206 and 1214 is 732042.

LCM(1206,1214) = 732042

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Least Common Multiple of 1206 and 1214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1206 and 1214, than apply into the LCM equation.

GCF(1206,1214) = 2
LCM(1206,1214) = ( 1206 × 1214) / 2
LCM(1206,1214) = 1464084 / 2
LCM(1206,1214) = 732042

Least Common Multiple (LCM) of 1206 and 1214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1206 and 1214. First we will calculate the prime factors of 1206 and 1214.

Prime Factorization of 1206

Prime factors of 1206 are 2, 3, 67. Prime factorization of 1206 in exponential form is:

1206 = 21 × 32 × 671

Prime Factorization of 1214

Prime factors of 1214 are 2, 607. Prime factorization of 1214 in exponential form is:

1214 = 21 × 6071

Now multiplying the highest exponent prime factors to calculate the LCM of 1206 and 1214.

LCM(1206,1214) = 21 × 32 × 671 × 6071
LCM(1206,1214) = 732042