Question

Find LCM using prime factorization method 46, 78
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Answer 1

Answer:

The lcm of 46 and 78 can be obtained like this:

The multiples of 46 are … , 1748, 1794, 1840, ….

The multiples of 78 are …, 1716, 1794, 1872, …

The common multiples of 46 and 78 are n x 1794, intersecting the two sets above, n\neq 0 \thinspace\in\thinspace\mathbb{Z}n =0∈Z.

In the intersection multiples of 46 ∩ multiples of 78 the least positive element is 1794.

Therefore, the least common multiple of 46 and 78 is 1794.

Answer 2

Answer:

Least Common Multiple of 46 and 78

Step-by-step explanation:

Least Common Multiple of 46 and 78 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 46 and 78, than apply into the LCM equation.

GCF(46,78) = 2

LCM(46,78) = ( 46 × 78) / 2

LCM(46,78) = 3588 / 2

LCM(46,78) = 1794

Least Common Multiple (LCM) of 46 and 78 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46 and 78. First we will calculate the prime factors of 46 and 78.

Prime Factorization of 46

Prime factors of 46 are 2, 23. Prime factorization of 46 in exponential form is:

46 = 21 × 231

Prime Factorization of 78

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

78 = 21 × 31 × 131

Now multiplying the highest exponent prime factors to calculate the LCM of 46 and 78.

LCM(46,78) = 21 × 231 × 31 × 131

LCM(46,78) = 1794

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