What is the Least Common Multiple of 77280 and 77292?
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 77280 and 77292 is 497760480.
LCM(77280,77292) = 497760480
Least Common Multiple of 77280 and 77292 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77280 and 77292, than apply into the LCM equation.
GCF(77280,77292) = 12
LCM(77280,77292) = ( 77280 × 77292) / 12
LCM(77280,77292) = 5973125760 / 12
LCM(77280,77292) = 497760480
Least Common Multiple (LCM) of 77280 and 77292 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 77280 and 77292. First we will calculate the prime factors of 77280 and 77292.
Prime Factorization of 77280
Prime factors of 77280 are 2, 3, 5, 7, 23. Prime factorization of 77280 in exponential form is:
77280 = 25 × 31 × 51 × 71 × 231
Prime Factorization of 77292
Prime factors of 77292 are 2, 3, 19, 113. Prime factorization of 77292 in exponential form is:
77292 = 22 × 32 × 191 × 1131
Now multiplying the highest exponent prime factors to calculate the LCM of 77280 and 77292.
LCM(77280,77292) = 25 × 32 × 51 × 71 × 231 × 191 × 1131
LCM(77280,77292) = 497760480
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