Least Common Multiple (LCM) of 172 and 61
The least common multiple (LCM) of 172 and 61 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 172 and 61?
First, calculate the GCD of 172 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 61 = 2 remainder 50 |
| 2 | 61 ÷ 50 = 1 remainder 11 |
| 3 | 50 ÷ 11 = 4 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 18 | 1530 |
| 152 and 138 | 10488 |
| 149 and 42 | 6258 |
| 11 and 198 | 198 |
| 163 and 98 | 15974 |