What is the Least Common Multiple of 322 and 342?
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 322 and 342 is 55062.
LCM(322,342) = 55062
Least Common Multiple of 322 and 342 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 322 and 342, than apply into the LCM equation.
GCF(322,342) = 2
LCM(322,342) = ( 322 × 342) / 2
LCM(322,342) = 110124 / 2
LCM(322,342) = 55062
Least Common Multiple (LCM) of 322 and 342 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 322 and 342. First we will calculate the prime factors of 322 and 342.
Prime Factorization of 322
Prime factors of 322 are 2, 7, 23. Prime factorization of 322 in exponential form is:
322 = 21 × 71 × 231
Prime Factorization of 342
Prime factors of 342 are 2, 3, 19. Prime factorization of 342 in exponential form is:
342 = 21 × 32 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 322 and 342.
LCM(322,342) = 21 × 71 × 231 × 32 × 191
LCM(322,342) = 55062
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