Least Common Multiple (LCM) of 121 and 167
The least common multiple (LCM) of 121 and 167 is 20207.
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 121 and 167?
First, calculate the GCD of 121 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 167 = 0 remainder 121 |
| 2 | 167 ÷ 121 = 1 remainder 46 |
| 3 | 121 ÷ 46 = 2 remainder 29 |
| 4 | 46 ÷ 29 = 1 remainder 17 |
| 5 | 29 ÷ 17 = 1 remainder 12 |
| 6 | 17 ÷ 12 = 1 remainder 5 |
| 7 | 12 ÷ 5 = 2 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 22 | 2354 |
| 162 and 113 | 18306 |
| 115 and 113 | 12995 |
| 156 and 112 | 4368 |
| 20 and 109 | 2180 |