Find Lowest Common Multiple (LCM) in Maths Grade 7 Maths Questions With Detailed Solutions

How to find the lowest common multiple (LCM) of two (or more) numbers in maths? Grade 7 maths questions are presented along with detailed solutions. Detailed Solutions and explanations are included.

What is the lowest common multiple (LCM) of two or more whole numbers?

It is the smallest whole number that is divisible by each of the numbers.
or
It is the smallest whole number that is multiple of those numbers.

Two Methods to Find the LCM

Method 1: May be used for small numbers
Examples: Find lowest common multiple of the numbers 6 and 8.
List the first few multiples of both numbers and stop as soon as you find a common multiple.
1) Multiply 6 by 1, 2, 3,.. to obtain the first few multiples of 6:
6, 12, 18, 24, 30, 36 ...
2) Multiply 8 by 1, 2, 3,.. to obtain the first few multiples of 8:
8, 16, 24,32 ,40 ...
Examine the multiples: The lowest common multiple of of 6 and 8 is 24.

Method 2: It uses prime factorization may be used for all numbers
Examples: Find lowest common multiple (LCM) of the numbers 42 and 60.
step 1 - The prime factorization of 42 is: 42 = 2 × 3 × 7
step 2 - The prime factorization of 60 is: 60 = 2^{ 2} × 3 × 5
step 3 - The LCM is given by product of all prime number in the prime factorization with the highest power.

What is the lowest common multiple of 180, 216 and 450?

a) Find the LCM and GCF of 12 and 16 and compare the products LCM(12,16)×GCF(12,16) and 12×16.
b) Find the LCM and GCF of 30 and 45 and compare the products LCM(30,45)×GCF(30,45) and 30×45.
c) Find the LCM and GCF of 60 and 160 and compare the products LCM(60,160)×GCF(60,160) and 60×160.