Question

What is the least common multiple of \[78\] and \[104\] ?

Answer 1

Hint: There are various methods for finding least common multiple of two given numbers. The simplest method to find the least common multiple is by prime factorization method. In the prime factorization method, we first represent the given two numbers as products of their prime factors and then find the product of all the factors counting the common factors only once.

Complete step-by-step answer:
To find the least common multiple of \[78\] and \[104\], first we find out the prime factors of both the numbers.
Prime factors of \[78\]$ = 2 \times 3 \times 13$
Prime factors of \[104\]$ = 2 \times 2 \times 2 \times 13$
$ = {2^3} \times 13$
Now, Least common multiple is a product of common factors with highest power and all other non-common factors. We can see that $2$ and $13$ is the only common factor of \[78\] and \[104\].
Hence, least common multiple of \[78\]and \[104\]$ = {2^3} \times 3 \times 13$
$ = 8 \times 3 \times 13 = 312$
Hence, the least common multiple of \[78\] and \[104\] is $312$.
So, the correct answer is “ $312$”.

Note: Highest common factor is the greatest number that divides both the given numbers. Similarly, the highest common factor can also be found by using the prime factorization method as well as using Euclid’s division lemma. Highest common divisor is just a product of common factors with lowest power. Highest common factor can also be calculated by division method as well as by using Euclid’s division lemma.