Least Common Multiple (LCM) of 172 and 63
The least common multiple (LCM) of 172 and 63 is 10836.
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 63?
First, calculate the GCD of 172 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 63 = 2 remainder 46 |
| 2 | 63 ÷ 46 = 1 remainder 17 |
| 3 | 46 ÷ 17 = 2 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 92 | 5980 |
| 56 and 198 | 5544 |
| 59 and 108 | 6372 |
| 36 and 80 | 720 |
| 146 and 49 | 7154 |