Least Common Multiple (LCM) of 127 and 167
The least common multiple (LCM) of 127 and 167 is 21209.
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 167?
First, calculate the GCD of 127 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 167 = 0 remainder 127 |
| 2 | 167 ÷ 127 = 1 remainder 40 |
| 3 | 127 ÷ 40 = 3 remainder 7 |
| 4 | 40 ÷ 7 = 5 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 29 | 2320 |
| 128 and 40 | 640 |
| 51 and 102 | 102 |
| 174 and 140 | 12180 |
| 35 and 145 | 1015 |