Least Common Multiple (LCM) of 72 and 155
The least common multiple (LCM) of 72 and 155 is 11160.
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 155?
First, calculate the GCD of 72 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 155 = 0 remainder 72 |
| 2 | 155 ÷ 72 = 2 remainder 11 |
| 3 | 72 ÷ 11 = 6 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 142 | 2130 |
| 83 and 31 | 2573 |
| 171 and 192 | 10944 |
| 149 and 135 | 20115 |
| 115 and 65 | 1495 |