LCM of 56 and 64 is 448. LCM stands for Lowest/Least Common multiple. It is the least positive integer that is divisible by the given set of numbers. Consider the example for finding the LCM of 56 and 64. The answer is 448. 448 is divisible by both 56 and 64. Even 896 is divisible by 56 and 64, however it is not the LCM for 56 and 64. The smaller number than 896 is 448 which is divisible by both 56 and 64. Hence 448 is the Least Common Multiple for 56 and 64. You can refer to LCM with Examples for better understanding.
What is LCM of 56 and 64
The Least Common Multiple or Lowest Common Multiple of 56 and 64 is 448.
How to Find LCM of 56 and 64?
LCM of 56 and 64 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 56 and 64 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 56 and 64 can be expressed as;
56 = 2 × 2 × 2 × 7
64 = 2 × 2 × 2 × 2 × 2 × 2
2 × 2 × 2 are the common factors of 56 and 64. The other factors of 56 and 64 are multiplied by the common factors of 56 and 64 for the LCM.
LCM (56, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 7 = 448
LCM of 56 and 64 Using Division Method
In the Division Method, 56 and 64 are divided by common prime divisors. When there are no common divisors, the division is continued by other divisors till the remainder becomes one. The product of these prime divisors forms LCM.
|
2 |
56 |
64 |
|
2 |
28 |
32 |
|
2 |
14 |
16 |
|
2 |
7 |
8 |
|
2 |
7 |
4 |
|
2 |
7 |
2 |
|
7 |
7 |
1 |
|
× |
1 |
1 |
LCM (56, 64) = 2 × 2 × 2 × 2 × 2 × 2 × 7 = 448
LCM of 56 and 64 Using Listing the Multiples
By listing all the multiples of 56 and 64, we can identify the least common multiple, which is the LCM. Below is the list of multiples for 56 and 64
|
Multiples of 56 |
Multiples of 64 |
|
56 |
64 |
|
112 |
128 |
|
168 |
192 |
|
224 |
256 |
|
280 |
320 |
|
336 |
384 |
|
392 |
448 |
|
448 |
512 |
|
504 |
576 |
LCM (56, 64) = 448
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 56 and 64?
Answer: 448 is the smallest number that is divisible by both 56 and 64.
What is the LCM of 2, 4, 8, 56 and 64?
Answer: The LCM of 2, 4, 8, 56 and 64 is 448.
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