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What is the Least Common Multiple of 1234 and 1253?

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 1234 and 1253 is 1546202.

LCM(1234,1253) = 1546202

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Least Common Multiple of 1234 and 1253 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1234 and 1253, than apply into the LCM equation.

GCF(1234,1253) = 1
LCM(1234,1253) = ( 1234 × 1253) / 1
LCM(1234,1253) = 1546202 / 1
LCM(1234,1253) = 1546202

Least Common Multiple (LCM) of 1234 and 1253 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1234 and 1253. First we will calculate the prime factors of 1234 and 1253.

Prime Factorization of 1234

Prime factors of 1234 are 2, 617. Prime factorization of 1234 in exponential form is:

1234 = 21 × 6171

Prime Factorization of 1253

Prime factors of 1253 are 7, 179. Prime factorization of 1253 in exponential form is:

1253 = 71 × 1791

Now multiplying the highest exponent prime factors to calculate the LCM of 1234 and 1253.

LCM(1234,1253) = 21 × 6171 × 71 × 1791
LCM(1234,1253) = 1546202