Least Common Multiple (LCM) of 128 and 72
The least common multiple (LCM) of 128 and 72 is 1152.
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 128 and 72?
First, calculate the GCD of 128 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 128 ÷ 72 = 1 remainder 56 |
| 2 | 72 ÷ 56 = 1 remainder 16 |
| 3 | 56 ÷ 16 = 3 remainder 8 |
| 4 | 16 ÷ 8 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 13 | 403 |
| 139 and 71 | 9869 |
| 121 and 163 | 19723 |
| 82 and 151 | 12382 |
| 143 and 120 | 17160 |