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184 LearnersLast updated on November 29th, 2024
LCM of 24 and 90
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 24 and 90?
We use LCM of 24 and 90, to find the smallest number that divides both the numbers equally. The smallest positive number is the number that divides both numbers equally, is 360 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 24 and 90?
The LCM of 24 and 90 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 24 and 90 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 both 24 and 90
- 2 divides 12 and not 45
- 5 divides 6 and not 45
- 3 divides both 3 and 45
- 3 divides 15
- 5 divides 5
Now multiply the divisors : 2×2×3×3×5×5=360 which is the LCM.
LCM of 24 and 90 using Listing multiples:
Step 1: Start by listing multiples of both the numbers separately:
Multiples of 24 are 24,48,72,96,120,144,168,192,216,240,264,288,312,336,360…..
Multiples of 90 are 90,180,270,360,450…..
Step 2: The least common factor from the list is 360.
Therefore, the LCM of 24 and 90 is 360.
LCM of 24 and 90 using Prime factorization:
Step 1:We part both the numbers unto factors:
Factor of 24: 23 × 31
Factors of 90: 32×5x2
Step 2:Take the powers of both the numbers and multiply together:
LCM=23x32x5=360.
Common Mistakes and How to Avoid Them in LCM of 24 and 90
LCM of 24 and 90 Examples
Problem 1
If the LCM of 24 and a number x is 360, find the value of x.
Explanation
Problem 2
Prove that the following relationship holds for 24 and 90: LCM (24,90) x GCD(24,90)= 24 × 90
Explanation
Problem 3
Two traffic lights blink at intervals of 24 seconds and 90 seconds, respectively. If both lights start blinking together, after how many seconds will they blink together again?
Explanation
Problem 4
A student organization meets every 24 days, and the parent-teacher organization meets every 90 days. When will both the organization meet together again?
Explanation
Problem 5
Simplify the expression:
Explanation
FAQ’s on LCM of 24 and 90
1.What is the GCF of 52 and 68?
2.How to find GCF?
3.Write the LCM of 12,24, and 90?
4.What is the LCM and GCF of 72 and 90?
5.How to find the LCM number by division method?
Important glossaries on the LCM of and 24
- 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 has the only positive divisor of them both as 1. For example, 6 and 7.
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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.
