LCM of 36, 42 and 72 is 504. 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 36, 42 and 72, 504 is the first(least or smallest) number that is common in the set of multiples of 36, 42 and 72. You can refer to Multiples.
What is LCM of 36, 42 and 72
The Least Common Multiple or Lowest Common Multiple of 36, 42 and 72 is 504.
How to Find LCM of 36, 42 and 72?
LCM of 36, 42 and 72 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36, 42 and 72 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 36, 42 and 72 can be expressed as;
36 = 2 × 2 × 3 × 3
42 = 2 × 3 × 7
72 = 2 × 2 × 2 × 3 × 3
Product of the union set of prime factors forms the LCM.
LCM (36, 48, 72) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 36, 42 and 72 Using Division Method
In the Division Method, the numbers 36, 42 and 72 are divided by prime divisors, starting from the smallest and preceding in the increasing order of divisibility. The remainder should be 1 for all the numbers and the product of the divisors forms the LCM.
|
2 |
36 |
42 |
72 |
|
2 |
18 |
21 |
36 |
|
2 |
9 |
21 |
18 |
|
3 |
9 |
21 |
9 |
|
3 |
3 |
7 |
3 |
|
7 |
1 |
7 |
1 |
|
× |
1 |
1 |
1 |
LCM (36, 48, 72) = 2 × 2 × 2 × 3 × 3 × 7 = 504
LCM of 36, 42 and 72 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 36, 42 and 72
Multiples of 36
36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576
Multiples of 42
42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588
Multiples of 72
72, 144, 216, 288, 360, 432, 504, 576, 648
LCM (36, 48, 72) = 504
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 36, 42 and 72?
Answer: 504 is the smallest number that is divisible by both 36, 42 and 72.
What is the LCM for 12, 36, 42 and 72?
Answer: LCM for 12, 36, 42 and 72 is 504.
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