LCM of 24 and 32 is 96. The smallest number among all frequent multiples of 24 and 32 is the LCM of 24 and 32. (24, 48, 72, 96, 120, 144, 168, etc.) and (32, 64, 96, 128, 160, etc.) are the first few multiples of 24 and 32, respectively. To find the LCM of 24 and 32, there are three typical methods: prime factorization, listing multiples, and division.The LCM of Two Numbers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 24 and 32?
The answer to this question is 96. The LCM of 24 and 32 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 32, is the smallest positive integer 96 which is divisible by both 24 and 32 with no remainder.
How to Find LCM of 24 and 32?
LCM of 24 and 32 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24 and 32 Using Prime Factorisation Method
The prime factorisation of 24 and 32, respectively, is given by:
24 = (2 × 2 × 2 × 3) = 23 × 31 and
32 = (2 × 2 × 2 × 2 × 2) = 25
LCM (24, 32) = 96
LCM of 24 and 32 Using Division Method
We’ll divide the numbers (24, 32) by their prime factors to get the LCM of 24 and 32 using the division method (preferably common). The LCM of 24 and 32 is calculated by multiplying these divisors.
|
2 |
24 |
36 |
|
2 |
12 |
16 |
|
2 |
6 |
8 |
|
2 |
3 |
4 |
|
2 |
3 |
2 |
|
3 |
3 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (24, 32) = 96
LCM of 24 and 32 Using Listing the Multiples
To calculate the LCM of 24 and 32 by listing out the common multiples, list the multiples as shown below:
|
Multiples of 24 |
Multiples of 32 |
|
24 |
32 |
|
48 |
64 |
|
72 |
96 |
|
96 |
128 |
|
120 |
160 |
The smallest common multiple of 24 and 32 is 96.
LCM (24, 32) = 96
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LCM of 24 and 32 Solved Example
Question: Verify the relationship between GCF and LCM of 24 and 32.
Solution: The relation between GCF and LCM of 24 and 32 is given as,
LCM(24, 32) × GCF(24, 32) = Product of 24, 32
Prime factorization of 24 and 32 is given as, 24 = (2 × 2 × 2 × 3) = 23 × 31 and 32 = (2 × 2 × 2 × 2 × 2) = 25
LCM(24, 32) = 96
GCF(24, 32) = 8
LHS = LCM(24, 32) × GCF(24, 32) = 96 × 8 = 768
RHS = Product of 24, 32 = 24 × 32 = 768
⇒ LHS = RHS = 768
Hence, verified.
Frequently Asked Questions on LCM of 24 and 32
What is the LCM of 24 and 32?
If the LCM of 32 and 24 is 96, Find its GCF.
Since the LCM of 32 and 24 = 96
⇒ 96 × GCF(32, 24) = 768.
Therefore, the greatest common factor (GCF) = 768/96 = 8.
If the LCM of 32 and 24 is 96, Find its GCF.
Since the LCM of 32 and 24 = 96
96 × GCF(32, 24) = 768
Therefore, the greatest common factor (GCF) = 768/96 = 8.
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