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 |
|---|---|
| 84 and 72 | 504 |
| 175 and 16 | 2800 |
| 56 and 134 | 3752 |
| 151 and 91 | 13741 |
| 185 and 33 | 6105 |