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What is the Least Common Multiple of 1512 and 1525?

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 1512 and 1525 is 2305800.

LCM(1512,1525) = 2305800

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Least Common Multiple of 1512 and 1525 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1512 and 1525, than apply into the LCM equation.

GCF(1512,1525) = 1
LCM(1512,1525) = ( 1512 × 1525) / 1
LCM(1512,1525) = 2305800 / 1
LCM(1512,1525) = 2305800

Least Common Multiple (LCM) of 1512 and 1525 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1512 and 1525. First we will calculate the prime factors of 1512 and 1525.

Prime Factorization of 1512

Prime factors of 1512 are 2, 3, 7. Prime factorization of 1512 in exponential form is:

1512 = 23 × 33 × 71

Prime Factorization of 1525

Prime factors of 1525 are 5, 61. Prime factorization of 1525 in exponential form is:

1525 = 52 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 1512 and 1525.

LCM(1512,1525) = 23 × 33 × 71 × 52 × 611
LCM(1512,1525) = 2305800