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What is the Least Common Multiple of 1692 and 1700?

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 1692 and 1700 is 719100.

LCM(1692,1700) = 719100

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Least Common Multiple of 1692 and 1700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1692 and 1700, than apply into the LCM equation.

GCF(1692,1700) = 4
LCM(1692,1700) = ( 1692 × 1700) / 4
LCM(1692,1700) = 2876400 / 4
LCM(1692,1700) = 719100

Least Common Multiple (LCM) of 1692 and 1700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1692 and 1700. First we will calculate the prime factors of 1692 and 1700.

Prime Factorization of 1692

Prime factors of 1692 are 2, 3, 47. Prime factorization of 1692 in exponential form is:

1692 = 22 × 32 × 471

Prime Factorization of 1700

Prime factors of 1700 are 2, 5, 17. Prime factorization of 1700 in exponential form is:

1700 = 22 × 52 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 1692 and 1700.

LCM(1692,1700) = 22 × 32 × 471 × 52 × 171
LCM(1692,1700) = 719100