Least Common Multiple (LCM) of 82 and 72
The least common multiple (LCM) of 82 and 72 is 2952.
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 82 and 72?
First, calculate the GCD of 82 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 72 = 1 remainder 10 |
| 2 | 72 ÷ 10 = 7 remainder 2 |
| 3 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 75 | 3675 |
| 150 and 59 | 8850 |
| 121 and 30 | 3630 |
| 76 and 110 | 4180 |
| 71 and 140 | 9940 |