Question

What is the least common multiple of \[8,10,12\]

Answer 1

Hint: In this question we have found the LCM of 8, 10 and 12. The LCM is the least common multiple and it is defined as \[LCM(a,b) = \dfrac{{\left| {a \cdot b} \right|}}{{\gcd (a,b)}}\] , where a and b are integers and \[\gcd \] is the greatest common divisor. We can find LCM by division method also.

Complete step by step solution:
Consider the given numbers 8, 10 and 12. Now we use the factors of each numbers to find the LCM of given numbers so we have
$ 8 = 2 \times 2 \times 2 $
$ 10 = 2 \times 5 $
$ 12 = 2 \times 2 \times 3 $
\[LCM = 2 \times 2 \times 2 \times 3 \times 5\]
\[ \Rightarrow LCM = 120\]
Therefore, the LCM of 8, 10 and 12 is 120.
If we have 3 numbers, we use a division method or prime factorisation to find the LCM. Suppose if we want to find LCM of 2 numbers, we use the formula and hence we obtain the solution.
So, the correct answer is “120”.

Note: We must know about the multiplication, division and tables of multiplication to solve the question. We should divide by the number by the least number and hence it is the correct way to solve the problem.