LCM of 48, 56 and 72 is 1008. The Least Common Divisor (LCD) also known as Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 48, 56 and 72, 1008 is the first(least or smallest) number that is common in the set of multiples of 48, 56 and 72. You can refer to Multiples.
What is LCM of 48, 56 and 72
The Least Common Multiple or Lowest Common Multiple of 48, 56 and 72 is 1008.
How to Find LCM of 48, 56 and 72?
LCM of 48, 56 and 72 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 48, 56 and 72 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 48, 56 and 72 can be expressed as;
48 = 2 × 2 × 2 × 2 × 3
56 = 2 × 2 × 2 × 7
72 = 2 × 2 × 2 × 3 × 3
Product of the prime factors that are both common and uncommon to 48, 56 and 72 forms the LCM.
LCM (48, 56, 72) = 2 × 2 × 2 × 2 × 3 × 3 × 7 = 1008
LCM of 48, 56 and 72 Using Division Method
In the Division Method, the given set of numbers 48, 56 and 72 are divided by prime divisors. When the remainders are 1, the division is considered complete. The product of all the divisors forms the LCM.
|
2 |
48 |
56 |
72 |
|
2 |
24 |
28 |
36 |
|
2 |
12 |
14 |
18 |
|
2 |
6 |
7 |
9 |
|
3 |
3 |
7 |
9 |
|
3 |
1 |
7 |
3 |
|
7 |
1 |
7 |
1 |
|
× |
1 |
1 |
1 |
LCM (48, 56, 72) = 2 × 2 × 2 × 2 × 3 × 3 × 7 = 1008
LCM of 48, 56 and 72 Using Listing the Multiples
By listing all the multiples of 48, 56 and 72, we can see the first common multiple, which is the LCM. Below is the list of multiples for 48, 56 and 72
Multiples of 48
48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576, 624, 672, 720, 768, 816, 864, 912, 960, 1008, 1056, 1104
Multiples of 56
56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784, 840, 896, 952, 1008, 1064, 1120
Multiples of 72
72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864, 936, 1008, 1080, 1152
LCM (48, 56, 72) = 1008
Related Articles
- LCM
- LCM Calculator
- LCM Formula
- LCM with Examples
- HCF and LCM
- Prime Factorization and Division method
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 48, 56 and 72?
Answer: 1008 is the smallest number that is divisible by both 48, 56 and 72.
What is the LCM for 12, 48, 56 and 72?
Answer: LCM for 12, 48, 56 and 72 is 1008.
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