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 |
|---|---|
| 170 and 105 | 3570 |
| 14 and 191 | 2674 |
| 101 and 112 | 11312 |
| 30 and 130 | 390 |
| 187 and 64 | 11968 |