Least Common Multiple (LCM) of 138 and 169
The least common multiple (LCM) of 138 and 169 is 23322.
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 169?
First, calculate the GCD of 138 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 169 = 0 remainder 138 |
| 2 | 169 ÷ 138 = 1 remainder 31 |
| 3 | 138 ÷ 31 = 4 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 145 | 27695 |
| 196 and 180 | 8820 |
| 174 and 136 | 11832 |
| 82 and 103 | 8446 |
| 81 and 17 | 1377 |