Last updated on May 26th, 2025
The meaning of least common factor (LCM) is to find the smallest number that divides any two integers evenly. LCM is used mainly in fractions to find a common number for both the integers. We use LCM for solving problems, lining up cycles or even synchronizing of events, also to schedule tasks in everyday life.
We use LCM of 18 and 32 to find the smallest number that divides both the numbers equally. The smallest positive number is the number that divides both numbers equally, is 288 without leaving any remainder. LCM is used mainly in fractions to find a common number for both the integers.
The LCM of 18 and 32 can be found by the following methods like division method, listing multiples, prime factorization.
In division method, we divide both the numbers, we begin with dividing side by side the smallest number. We continue dividing until we get a common number that divides both the numbers equally. It makes it easier for the children to focus on prime factors and identify them.
Now multiply the divisors : 2×2×2×2×3×3=288 which is the LCM.
Step 1: Start by listing multiples of both the numbers separately:
Multiples of 18 are 18,36,54,72,90,108,126,144,162,180,198,216,234,252,270,288…..
Multiples of 32 are 32,64,96,128,160,192,224,256,288…..
Step 2: The least common factor from the list is 288. Therefore, the LCM of 18 and 32 is 288.
Step 1: We part both the numbers unto factors:
Factor of 18: 2×32
Factors of 32: 25
Step 2:Take the powers of both the numbers and multiply together:
LCM= 25 × 32 =288.
While solving problems based on the LCM of 18 and 32, children fail to understand few concepts, to give an idea of the mistakes, given below are a few mistakes and solutions of how to avoid them:
Find the LCM of 18 and 32 using prime Factorization.
LCM(18,32) = 288
18= 2 × 32
32=25
LCM= 25 × 32 = 32 × 9=288.
Find the missing number if LCM(18,X)=144 and X<32.
LCM(18,X)
= 24 × 32
=144
X=16.
missing number is 16.
Find the smallest number that, when multiplied by 18, gives an LCM with 32 of 288.
the smallest number is 9.
32=25, and 288=25×32.
The missing factor is 9, so the smallest number is 9.
Given LCM(a,32) = 288 and a= 18, verify the formula LCM(a, b)×GCD(a, b)=a × b.
288 × 2 = 18 × 32 =576.
Verified.
both sides are equal. hence verified.
Simplify the fraction 144/LCM (18,32)
LCM(18,32)=288
144/288= 1/2.
we already know the LCM(18,32)=288
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.