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What is the Least Common Multiple of 1292 and 1300?

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 1292 and 1300 is 419900.

LCM(1292,1300) = 419900

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Least Common Multiple of 1292 and 1300 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1292 and 1300, than apply into the LCM equation.

GCF(1292,1300) = 4
LCM(1292,1300) = ( 1292 × 1300) / 4
LCM(1292,1300) = 1679600 / 4
LCM(1292,1300) = 419900

Least Common Multiple (LCM) of 1292 and 1300 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1292 and 1300. First we will calculate the prime factors of 1292 and 1300.

Prime Factorization of 1292

Prime factors of 1292 are 2, 17, 19. Prime factorization of 1292 in exponential form is:

1292 = 22 × 171 × 191

Prime Factorization of 1300

Prime factors of 1300 are 2, 5, 13. Prime factorization of 1300 in exponential form is:

1300 = 22 × 52 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 1292 and 1300.

LCM(1292,1300) = 22 × 171 × 191 × 52 × 131
LCM(1292,1300) = 419900