Least Common Multiple (LCM) of 72 and 108
The least common multiple (LCM) of 72 and 108 is 216.
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 108?
First, calculate the GCD of 72 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 108 = 0 remainder 72 |
| 2 | 108 ÷ 72 = 1 remainder 36 |
| 3 | 72 ÷ 36 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 20 | 340 |
| 51 and 23 | 1173 |
| 187 and 189 | 35343 |
| 28 and 188 | 1316 |
| 32 and 41 | 1312 |