Question

Find the LCM of 45 ,105 ,165

Answer 1

Answer:

Step-by-step explanation:

Given,

45,105 and 165

105 = 3×5×7

165 = 3×5×11

45 = 3×5×3

LCM of 45,105 and 165 is

= 3×5×7×11×3

= 3465

Therefore,the LCM of given numbers is 3465.

Answer 2

Concept

In mathematics, the LCM of any two values ​​is the value that is  divisible by the two given numbers. The full form of LCM is Least Common Multiple. Also known as the Least Common Divisor (LCD).

Given

We have been given three numbers 45 , 105 , 165 .

Find

We are asked to determine the LCM of the given three numbers .

Solution

For finding LCM , we will do the prime factorization of given numbers.

$45=3\times\imes3\times5\\105=3\times\imes5\times7\\165=3\times\imes5\times11$

Now writing the prime factors of all the three numbers together, we get

$45\times105\times165=3\times\imes3\times5\times3\times\imes5\times7\\\times3\times\imes5\times11$

Now pairing the common prime factors we get the LCM .

Hence, there are two pair of  3’s and one pair of 5's .

So the LCM of 45, 105 and 165 will be $=3\times3\times5\times7\times11$

                                                                 $=3465$

Therefore , the LCM of the given numbers is 3456 .

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