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What is the Least Common Multiple of 690 and 699?

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 690 and 699 is 160770.

LCM(690,699) = 160770

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Least Common Multiple of 690 and 699 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 690 and 699, than apply into the LCM equation.

GCF(690,699) = 3
LCM(690,699) = ( 690 × 699) / 3
LCM(690,699) = 482310 / 3
LCM(690,699) = 160770

Least Common Multiple (LCM) of 690 and 699 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 690 and 699. First we will calculate the prime factors of 690 and 699.

Prime Factorization of 690

Prime factors of 690 are 2, 3, 5, 23. Prime factorization of 690 in exponential form is:

690 = 21 × 31 × 51 × 231

Prime Factorization of 699

Prime factors of 699 are 3, 233. Prime factorization of 699 in exponential form is:

699 = 31 × 2331

Now multiplying the highest exponent prime factors to calculate the LCM of 690 and 699.

LCM(690,699) = 21 × 31 × 51 × 231 × 2331
LCM(690,699) = 160770