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What is the Least Common Multiple of 69 and 77?

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 69 and 77 is 5313.

LCM(69,77) = 5313

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Least Common Multiple of 69 and 77 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69 and 77, than apply into the LCM equation.

GCF(69,77) = 1
LCM(69,77) = ( 69 × 77) / 1
LCM(69,77) = 5313 / 1
LCM(69,77) = 5313

Least Common Multiple (LCM) of 69 and 77 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69 and 77. First we will calculate the prime factors of 69 and 77.

Prime Factorization of 69

Prime factors of 69 are 3, 23. Prime factorization of 69 in exponential form is:

69 = 31 × 231

Prime Factorization of 77

Prime factors of 77 are 7, 11. Prime factorization of 77 in exponential form is:

77 = 71 × 111

Now multiplying the highest exponent prime factors to calculate the LCM of 69 and 77.

LCM(69,77) = 31 × 231 × 71 × 111
LCM(69,77) = 5313

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