212 LearnersLast updated on May 26th, 2025
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
While solving problems based on the LCM of 24 and 90, 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:
Mistake 1
Stopping the division method way too soon.
Students sometimes stop dividing very soon, when they are not able to divide both the numbers with the same number. For example, we can divide 24 by 2, but 90 isn't divisible by 2. To continue the dividing method until all the factors are found. The students should continue dividing until they find the common number that divides both the integers.
LCM of 24 and 90 Examples
Problem 1
If the LCM of 24 and a number x is 360, find the value of x.
Answer: x=90
Explanation
LCM (a, b) x GCD(a, b)=axb
LCM(24,x)=360
a=24
GCD(24,x)=6(since x shares factors with 24)
By using the formula:
360 x 6 = 24 x x
2160=24x x
x = 2160/24=90
Problem 2
Prove that the following relationship holds for 24 and 90: LCM (24,90) x GCD(24,90)= 24 × 90
Prime factorization:
24= 23 × 3
90= 2 × 32 × 5
LCM (24,90):
Select highest powers of all prime factors:
23 × 32 × 5 =360.
GCD (24,90):
Take LCM of the common factors:
2 × 3=6
Verifying the relationship:
LCM (24,90) x GCD(24,90)= 360 × 6=2160
24 × 90 = 2160
Explanation
Both sides are equal.
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?
To find when the two lights will blink together, we need to calculate the LCM of the numbers 24and 90
LCM of 24 and 90
Prime factors of 24: 23× 3
Prime factors of 90: 32×5x2
LCM = 23×32×5=360
Explanation
Therefore, the two lights will blink together again after 360 seconds.
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?
LCM of 24and 90
Prime factors of 24 : 23×3
Prime factors of 90: 32 × 2 × 5
LCM = 23×32×5=360
Explanation
The two lights will blink together again after 360 seconds.
Problem 5
Simplify the expression:
solution:
24/360+90/360
Simplify each fraction 24/360 =1/15 , 90/360= 1/4
Add the fractions 1/15+1/4
LCM(15,4)=60, rewriting them we get,
1/15=4/60 , 1/4=15/60
Add the fractions:
4/60+15/60=19/60
Explanation
Thus, the simplified expression is: 19/60
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?
6.How can children in United States use numbers in everyday life to understand LCM of 24 and 90?
7.What are some fun ways kids in United States can practice LCM of 24 and 90 with numbers?
8.What role do numbers and LCM of 24 and 90 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 24 and 90 skills?
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.
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