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What is the Least Common Multiple of 1688 and 1706?

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 1706 is 1439864.

LCM(1688,1706) = 1439864

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Least Common Multiple of 1688 and 1706 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 1706, than apply into the LCM equation.

GCF(1688,1706) = 2
LCM(1688,1706) = ( 1688 × 1706) / 2
LCM(1688,1706) = 2879728 / 2
LCM(1688,1706) = 1439864

Least Common Multiple (LCM) of 1688 and 1706 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1688 and 1706. First we will calculate the prime factors of 1688 and 1706.

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 1706

Prime factors of 1706 are 2, 853. Prime factorization of 1706 in exponential form is:

1706 = 21 × 8531

Now multiplying the highest exponent prime factors to calculate the LCM of 1688 and 1706.

LCM(1688,1706) = 23 × 2111 × 8531
LCM(1688,1706) = 1439864