Question

Find the least common multiple of 9, 36, 45?

Answer 1

Hint:Here, we'll use the prime factorization method to discover the factors of each integer independently. Then we'll make a list of all the numbers' factors. We'll find the needed values using the LCM concepts. Prime factorization is a technique for determining the prime factors of a set of integers.

Complete step by step answer:
The least common multiple is the smallest number that divides two or more numbers exactly.
We express each number as a product of prime numbers to obtain the LCM of the given numbers. The LCM is the product of the highest power of the prime numbers that appear in prime factorization of any number.
We will find the prime factors of 8, 36, 45 respectively
We will expand 9 as product of prime numbers
$9 = 3 \times 3$ (1)
We will expand 36 as product of prime numbers
$36 = 2 \times 2 \times 3 \times 3$ (2)
We will expand 45 as product of prime numbers
$45 = 3 \times 3 \times 5$ (3)
We can conclude from equations 1, 2 and 3 that we have common factors as two 3’s while an extra factor is two 2’s in 36 and one 5 in 845.
So, the L.C.M. of 9,36 and 45 is
L.C.M of 9,36 and 45 $ = 3 \times 3 \times 2 \times 2 \times 5$
L.C.M of 9,36 and 45 $ = 180$
Hence, the L.C.M. of 9, 36 and 45 is 180.

Note: The concepts of the least common multiple and the greatest common factor must be understood. The LCM is a number that can be divided by the four numbers supplied, but the HCF is a number that divides all four numbers given. It's helpful to write the prime factorizations of the integers clearly so we don't make any tiny mistakes and get the right result.