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What is the Least Common Multiple of 78 and 98?

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 78 and 98 is 3822.

LCM(78,98) = 3822

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Least Common Multiple of 78 and 98 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78 and 98, than apply into the LCM equation.

GCF(78,98) = 2
LCM(78,98) = ( 78 × 98) / 2
LCM(78,98) = 7644 / 2
LCM(78,98) = 3822

Least Common Multiple (LCM) of 78 and 98 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78 and 98. First we will calculate the prime factors of 78 and 98.

Prime Factorization of 78

Prime factors of 78 are 2, 3, 13. Prime factorization of 78 in exponential form is:

78 = 21 × 31 × 131

Prime Factorization of 98

Prime factors of 98 are 2, 7. Prime factorization of 98 in exponential form is:

98 = 21 × 72

Now multiplying the highest exponent prime factors to calculate the LCM of 78 and 98.

LCM(78,98) = 21 × 31 × 131 × 72
LCM(78,98) = 3822

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