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What is the Least Common Multiple of 693 and 700?

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 693 and 700 is 69300.

LCM(693,700) = 69300

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Least Common Multiple of 693 and 700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 693 and 700, than apply into the LCM equation.

GCF(693,700) = 7
LCM(693,700) = ( 693 × 700) / 7
LCM(693,700) = 485100 / 7
LCM(693,700) = 69300

Least Common Multiple (LCM) of 693 and 700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 693 and 700. First we will calculate the prime factors of 693 and 700.

Prime Factorization of 693

Prime factors of 693 are 3, 7, 11. Prime factorization of 693 in exponential form is:

693 = 32 × 71 × 111

Prime Factorization of 700

Prime factors of 700 are 2, 5, 7. Prime factorization of 700 in exponential form is:

700 = 22 × 52 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 693 and 700.

LCM(693,700) = 32 × 71 × 111 × 22 × 52
LCM(693,700) = 69300