Least Common Multiple (LCM) of 61 and 172
The least common multiple (LCM) of 61 and 172 is 10492.
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 61 and 172?
First, calculate the GCD of 61 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 172 = 0 remainder 61 |
| 2 | 172 ÷ 61 = 2 remainder 50 |
| 3 | 61 ÷ 50 = 1 remainder 11 |
| 4 | 50 ÷ 11 = 4 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 182 | 1638 |
| 82 and 131 | 10742 |
| 45 and 68 | 3060 |
| 167 and 135 | 22545 |
| 20 and 69 | 1380 |