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158 LearnersLast updated on November 30th, 2024
LCM of 18 and 48
The smallest number that should also be a positive number, and evenly divide both the numbers, is known as the least common factor. LCM is very important for solving problems, especially fractions, scheduling events etc.
What is the LCM of 18 and 48
The LCM of 18 and 48 is the lowest number that divides both 18 and 48 without leaving any remainder. The LCM of 18 and 48 is 144.
How to find the LCM of 18 and 48?
The LCM of 18 and 48 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 18 and 48 using Division method:
In the division method, we divide both the numbers by the lowest possible number until we get 1 for both numbers.
2 divides 18 and 48, leaving 9,24
2 divides 24 and not 9, leaving 12,9
3 divides 12 and 9, leaving 4,3
3 divides 3 and not 4, leaving 1,4
4 divides 4 leaving 1
LCM = 4 × 2 × 3 × 3= 144.
LCM of 18 and 48 using Listing multiples:
We write the multiples of both numbers till we find the common one.
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162…
Multiples of 48: 48, 96, 144, 192…
The common multiple is 30. So, the LCM of 18 and 48 is 144.
LCM of 18 and 48 using prime factorization:
We part each number into divisors and select the highest powers of all the prime factors.
18= 2×3×3
48= 2×2×2×2 × 3×3
LCM = 24 × 32= 144.
Common Mistakes and How to Avoid Them in LCM of 18 and 48
Examples of LCM of 18 and 48
Problem 1
Given that the LCM of 18 and another number X is 144. Find the value of X.
Explanation
Problem 2
Solve the following expression using LCM of 18 and 48: 5/18 + 7/48
Explanation
Problem 3
Verify the prime factorization of LCM(3,10) using their prime factors.
Explanation
Problem 4
Solve the system of equations: x+y=66 and LCM(x, y)=144, find the value of x and y.
Explanation
Problem 5
Find two positive integers whose LCM is 144 and whose sum is minimized.
Explanation
FAQ’s on LCM of 18 and 48
1.What is the GCF of 12 and 100?
2.How many distinct prime factors does 36 have?
3.What are the first five composite numbers?
4.What is the smallest odd prime number?
5.How many multiples are there between 10 and 250?
Important glossaries for LCM of 18 and 48
- Co-prime: two numbers that have only one number that is 1 as their common factor. For example, 8 and 15 are co-prime numbers.
- Even Number: A natural number is divisible by 2. For example, 2,4,68,10 etc.
- Prime Factorization: The process of parting down a number into its prime factors is called Prime Factorization. For example, prime factorization of 24 = 2 × 2 × 2 × 3.
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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.
