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What is the Least Common Multiple of 1510 and 1514?

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 1510 and 1514 is 1143070.

LCM(1510,1514) = 1143070

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Least Common Multiple of 1510 and 1514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1510 and 1514, than apply into the LCM equation.

GCF(1510,1514) = 2
LCM(1510,1514) = ( 1510 × 1514) / 2
LCM(1510,1514) = 2286140 / 2
LCM(1510,1514) = 1143070

Least Common Multiple (LCM) of 1510 and 1514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1510 and 1514. First we will calculate the prime factors of 1510 and 1514.

Prime Factorization of 1510

Prime factors of 1510 are 2, 5, 151. Prime factorization of 1510 in exponential form is:

1510 = 21 × 51 × 1511

Prime Factorization of 1514

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

1514 = 21 × 7571

Now multiplying the highest exponent prime factors to calculate the LCM of 1510 and 1514.

LCM(1510,1514) = 21 × 51 × 1511 × 7571
LCM(1510,1514) = 1143070