157 LearnersLast updated on May 26th, 2025
LCM of 24 and 32
By ascertaining the LCM of the numbers we can simplify the arithmetic operations with fractions by equating the denominators and in other mathematical scenarios. The smallest positive integer and a multiple of both 24 and 30, is the LCM of the numbers.
What is the LCM of 24 and 32?
By ascertaining the LCM of the numbers we can simplify the arithmetic operations with fractions by equating the denominators and in other mathematical scenarios. The smallest positive integer and a multiple of both 25 and 32, is the LCM of the numbers.
How to Find the LCM of 24 and 32?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 24 and 32 using the Listing Multiples Method
The LCM of 24 and 32 can be calculated using the following steps:
Step1:Write down the multiples of each number
Multiples of 24 =24,48,72,96,144,…
Multiples of 32 = 32,64,96,…
Step1: Ascertain the smallest multiple from the listed multiples:
The smallest common multiple is 96.
Thus, LCM(24,32) = 96
LCM of 24 and 32 using the Prime Factorization Method
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Step1: Find the prime factors of each number:
32 = 2×2×2×2×2
24 = 2×2×2×3
Step2: Take the highest powers of each prime factor and multiply the highest powers to get the LCM:
LCM(32,24) = 96
LCM of 24 and 32 using the Division Method
In the division method we, divide the numbers by their common prime factors and multiplying the divisors to find the LCM.
Step 1: Write the numbers, divide by common prime factors and multiply the divisors.
Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
Step 3:The LCM of the numbers is the product of the prime numbers in the first column, i.e,
Thus, LCM(32,24) = 96
Common Mistakes and how to avoid them in LCM of 24 and 32
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 24 and 32 make a note while practicing.
Mistake 1
Confusing between LCM and HCF of the numbers 24 and 32
It is common for one to be confused between the HCF (Highest common factor) and LCM (least common multiple). LCM is the smallest number divisible by 24 and 32 while, the largest number that divides them both is the HCF.
LCM of 24 and 32 Examples
Problem 1
a=24, b=32. Express the LCM of the numbers a and b as a function of the prime factorization of the digits. Prove that the method used works universally for any pair of integers.
The prime factorization of a and b;
a = 23×31
b = 25
Pick the maximum powers of the primes;
LCM(a,b) = 25×31
LCM = 96, using prime factorization.
Explanation
The LCM of any two numbers is the smallest number that is divisible by them both. When we prime factorize, we make sure that all the factors are accounted for and the highest power of each prime is selected. By doing so, we ensure that the resultant number is divisible by both a and b.
This method works universally, for all/any two given numbers as it is based on the principle that divisibility is to be ensured by combining prime factors in their highest powers.
Problem 2
Traffic light A changes every 32 minutes and traffic light B switches every 24 minutes. When will they next turn green simultaneously.
We use the formula;
LCM(a, b) = a×b/HCF(a, b) where, a=32, b=24
HCF of 24 and 32;
Factors of 32 = 1,2,4,8,16,32
Factors of 24 = 1,2,3,4,6,8,12,24
HCF(32,24)= 8
Applying the ascertained HCF in the formula;
LCM(a, b) = a×b/HCF(a, b)
LCM(32,24) = 32×24/8 = 96
LCM(32,24) = 96
Explanation
The traffic lights will change simultaneously in 96 minutes.
Problem 3
LCM of 24x and 32x2 is 96xn. Find n.
First, we find the LCM of 24 and 32 (numerical coefficients)
Prime factorize the numbers;
32 = 2×2×2×2×2
24= 2×2×2×3
LCM(24,32) = 96
For variables x and x2, the highest power of x is taken by the LCM, therefore we take x2.
I.e., LCM (24x,32x2) = 96x2
By comparing 96xn, we have
xn=x2
n= 2
Explanation
By taking the highest power of each variable involved, we find the LCM of the variable powers.
n=2.
FAQs on LCM of 24 and 32
1.What is the HCF of 24 and 32?
2.What is the LCM of 36 and 24?
3.What is the LCM of 32 and 40?
4.What is the LCM of 8, 32 and 24?
5.What is the LCM of 32,24 and 72?
6.How can children in Indonesia use numbers in everyday life to understand LCM of 24 and 32?
7.What are some fun ways kids in Indonesia can practice LCM of 24 and 32 with numbers?
8.What role do numbers and LCM of 24 and 32 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve LCM of 24 and 32 skills?
Important glossaries for the LCM of 24 and 32
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: Process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers:Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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Hiralee Lalitkumar Makwana
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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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