Question

The L.C.M. of 148 and 185 is
1) 680
2) 749
3) 3700
4) 2960

Answer 1

Hint: The least common multiple or L.C.M. of two numbers say $a$ and $b$, is the smallest possible number that is divisible by both $a$ and b. To find the lcm of 148 and 185, we have to prime factorise both the numbers. Select the factors with their highest power among the two and multiply them to find the required L.C.M.

Complete step-by-step answer:
The least common multiple or L.C.M. of two numbers, say $a$ and $b$, is the smallest possible number that is divisible by both $a$ and $b$. The first step is to factorise the number into prime factors.
The prime factorisation of 148 is $2 \times 2 \times 37 = {2^2}\left( {37} \right)$, and of 185 is $5\left( {37} \right)$.
Select the prime factors with their highest power among the two.
From the prime factorisation of 148 and 185, we can say that there are a total of 3 unique prime factors that are 2,5 and 37.
The highest power of 2 among the prime factorisation of 148 and 185 is 2, highest power of 5 among the prime factorisation of 148 and 185 is 1 and the highest power of 37 among the prime factorisation of 148 and 185 is 1.
The L.C.M. can be calculated by multiplying the unique prime factors raised to their highest power among the two numbers. Thus L.C.M. of 148 and 185 is ${2^2}\left( 5 \right)\left( {37} \right)$
On multiplying we get L.C.M. of 148 and 185 is 740.
Hence option B is the correct answer.

Note: The prime factors selected for multiplication must be unique, and if they are repeated then the highest power among the numbers should be chosen. The L.C.M. of two positive numbers can never be less than either of those numbers. If the bigger number is multiple of smaller numbers, then the L.C.M. is the bigger number.