Least Common Multiple (LCM) of 138 and 167
The least common multiple (LCM) of 138 and 167 is 23046.
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 138 and 167?
First, calculate the GCD of 138 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 167 = 0 remainder 138 |
| 2 | 167 ÷ 138 = 1 remainder 29 |
| 3 | 138 ÷ 29 = 4 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 32 | 1952 |
| 111 and 43 | 4773 |
| 187 and 186 | 34782 |
| 138 and 180 | 4140 |
| 54 and 78 | 702 |