Question

Find the L.C.M of 2, 5.

Answer 1

Hint: prime factorization method means splitting the given number in terms of prime factors. We know that the number which exactly divides two or more numbers is called the common factor. From all the prime factors of the given number, identify the maximum number of times each prime factor appears. This is called LCM or least common multiple.

Complete step-by-step answer:
Using prime factorization method
(1).2, 5
Factor of \[2=1\times 2\]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)
Factor of \[5=1\times 5\]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(2)
We have to take the maximum number of times each prime factor appears; this is the least common multiple or else called as L.C.M of the given numbers.
\[L.C.M\left( 2,5 \right)=2\times 5=10\]. . . . . . . . . . . . . . . (3)

Note: LCM can also be found using the division method by dividing the given numbers by using least common prime factor and continue till there is no more prime factor. Then multiply all the divisors. HCF can also be found using a division method. In this method divide the largest number by the smallest number of the given numbers until the remainder is zero. The last divisor will be HCF of given numbers.