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What is the Least Common Multiple of 1688 and 1704?

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 1688 and 1704 is 359544.

LCM(1688,1704) = 359544

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Least Common Multiple of 1688 and 1704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1688 and 1704, than apply into the LCM equation.

GCF(1688,1704) = 8
LCM(1688,1704) = ( 1688 × 1704) / 8
LCM(1688,1704) = 2876352 / 8
LCM(1688,1704) = 359544

Least Common Multiple (LCM) of 1688 and 1704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1688 and 1704. First we will calculate the prime factors of 1688 and 1704.

Prime Factorization of 1688

Prime factors of 1688 are 2, 211. Prime factorization of 1688 in exponential form is:

1688 = 23 × 2111

Prime Factorization of 1704

Prime factors of 1704 are 2, 3, 71. Prime factorization of 1704 in exponential form is:

1704 = 23 × 31 × 711

Now multiplying the highest exponent prime factors to calculate the LCM of 1688 and 1704.

LCM(1688,1704) = 23 × 2111 × 31 × 711
LCM(1688,1704) = 359544