Least Common Multiple (LCM) of 72 and 165
The least common multiple (LCM) of 72 and 165 is 3960.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 72 and 165?
First, calculate the GCD of 72 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 165 = 0 remainder 72 |
| 2 | 165 ÷ 72 = 2 remainder 21 |
| 3 | 72 ÷ 21 = 3 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 124 and 173 | 21452 |
| 77 and 17 | 1309 |
| 121 and 62 | 7502 |
| 181 and 24 | 4344 |
| 81 and 182 | 14742 |