LCM of 48 and 64 is 192. LCM defines the least number which is exactly divisible by two or more numbers. The article Prime Factorisation and Division Method for LCM and HCF is formulated by expert teachers to help students in finding out the LCM and HCF of given numbers quickly and hence reduce the time during the examination. Students are recommended to follow this article for effective exam preparation once they are done with the complete syllabus. Let us learn how to determine the least common multiple of 48 and 64 in simple language here.
What is LCM of 48 and 64?
The Least Common Multiple of 48 and 64 is 192.
How to Find LCM of 48 and 64?
LCM of 48 and 64 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 48 and 64 Using Prime Factorisation Method
Here, the given natural numbers are expressed as the product of prime factors. Hence the numbers 48 and 64 are written as;
48 = 2 × 2 × 2 × 2 × 3
64 = 2 × 2 × 2 × 2 × 2 × 2
LCM (48, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192
LCM of 48 and 64 Using Division Method
In this method, to calculate the LCM, we divide the numbers 48 and 64 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 48 and 64.
| 2 | 48 | 64 |
| 2 | 24 | 32 |
| 2 | 12 | 16 |
| 2 | 6 | 8 |
| 2 | 3 | 4 |
| 2 | 3 | 2 |
| 3 | 3 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (48, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 192
LCM of 48 and 64 Using Listing the Multiples
Here, we list the multiples of 48 and 64 to determine the LCM. Check the multiples of 48 and 64 from the table given below.
| Multiples of 48 | Multiples of 64 |
| 48 | 64 |
| 96 | 128 |
| 144 | 192 |
| 192 | 256 |
| 240 | 320 |
LCM (48, 64) = 192
Related Articles
Video Lesson on Applications of LCM
Solved Example
Question: What is the smallest number that is divisible by both 48 and 64?
Solution: The smallest number that is divisible by both 48 and 64 is their LCM. The LCM of 48 and 64 is 192. Therefore the smallest number that is divisible by both 48 and 64 is 192.
Frequently Asked Questions on LCM of 48 and 64
What is the LCM of 48 and 64?
Is the LCM of 48 and 64 the same as the HCF of 48 and 64?
15 is the HCF of 48 and 64. True or False.
List the methods used to find the LCM of 48 and 64.
The following methods are used to find the LCM of 48 and 64
Prime Factorisation
Division Method
Listing the Multiples
Write the relation between GCF and LCM of 48 and 64.
The relation between GCF and LCM of 48 and 64 is
GCF × LCM = 48 × 64
GCF × LCM = 3072
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