Table Of Contents
152 LearnersLast updated on November 29th, 2024
LCM of 18 and 32
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.
What is the LCM of 18 and 32?
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.
How to find the LCM of 18 and 32?
The LCM of 18 and 32 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 18 and 32 using Division method:
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.
- 2 divides 18 and 32
- 2 divides 9 and 16
- 2 divides 8 and not 9
- 2 divides 4 and not 9
- 2 divides 2, and not 9
- 3 divides 9
- 3 decides 3.
Now multiply the divisors : 2×2×2×2×3×3=288 which is the LCM.
LCM of 18 and 32 using Listing multiples:
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.
LCM of 18 and 32 using Prime factorization:
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.
Common Mistakes and How to Avoid Them in LCM of 18 and 32
LCM of 18 and 32 Examples
Problem 1
Find the LCM of 18 and 32 using prime Factorization.
Explanation
Problem 2
Find the missing number if LCM(18,X)=144 and X<32.
Explanation
Problem 3
Find the smallest number that, when multiplied by 18, gives an LCM with 32 of 288.
Explanation
Problem 4
Given LCM(a,32) = 288 and a= 18, verify the formula LCM(a, b)×GCD(a, b)=a × b.
Explanation
Problem 5
Simplify the fraction 144/LCM (18,32)
Explanation
FAQs on LCM of 18 and 32
1.What are the expanded factors of 108?
2. What is the prime factor tree for 200?
3.Which number is not a factor of 32?
4.Is 1 considered as the GCF?
5.What is a relatively prime number?
Important glossaries on the LCM of 18 and 32
- Prime Factor: A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2×7.
- Co-prime numbers: numbers which have the only positive divisor of them both as 1. For example, 6 and 7.
Explore More numbers
Previous to LCM of 18 and 32
Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
