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What is the Least Common Multiple of 1514 and 1524?

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 1514 and 1524 is 1153668.

LCM(1514,1524) = 1153668

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Least Common Multiple of 1514 and 1524 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1514 and 1524, than apply into the LCM equation.

GCF(1514,1524) = 2
LCM(1514,1524) = ( 1514 × 1524) / 2
LCM(1514,1524) = 2307336 / 2
LCM(1514,1524) = 1153668

Least Common Multiple (LCM) of 1514 and 1524 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1514 and 1524. First we will calculate the prime factors of 1514 and 1524.

Prime Factorization of 1514

Prime factors of 1514 are 2, 757. Prime factorization of 1514 in exponential form is:

1514 = 21 × 7571

Prime Factorization of 1524

Prime factors of 1524 are 2, 3, 127. Prime factorization of 1524 in exponential form is:

1524 = 22 × 31 × 1271

Now multiplying the highest exponent prime factors to calculate the LCM of 1514 and 1524.

LCM(1514,1524) = 22 × 7571 × 31 × 1271
LCM(1514,1524) = 1153668