Least Common Multiple (LCM) of 57 and 72
The least common multiple (LCM) of 57 and 72 is 1368.
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 57 and 72?
First, calculate the GCD of 57 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 72 = 0 remainder 57 |
| 2 | 72 ÷ 57 = 1 remainder 15 |
| 3 | 57 ÷ 15 = 3 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 24 | 2328 |
| 60 and 121 | 7260 |
| 111 and 33 | 1221 |
| 136 and 65 | 8840 |
| 108 and 100 | 2700 |