Least Common Multiple (LCM) of 127 and 172
The least common multiple (LCM) of 127 and 172 is 21844.
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 127 and 172?
First, calculate the GCD of 127 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 172 = 0 remainder 127 |
| 2 | 172 ÷ 127 = 1 remainder 45 |
| 3 | 127 ÷ 45 = 2 remainder 37 |
| 4 | 45 ÷ 37 = 1 remainder 8 |
| 5 | 37 ÷ 8 = 4 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 21 | 1092 |
| 35 and 33 | 1155 |
| 105 and 154 | 2310 |
| 176 and 33 | 528 |
| 105 and 124 | 13020 |