Least Common Multiple (LCM) of 126 and 169
The least common multiple (LCM) of 126 and 169 is 21294.
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 126 and 169?
First, calculate the GCD of 126 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 169 = 0 remainder 126 |
| 2 | 169 ÷ 126 = 1 remainder 43 |
| 3 | 126 ÷ 43 = 2 remainder 40 |
| 4 | 43 ÷ 40 = 1 remainder 3 |
| 5 | 40 ÷ 3 = 13 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 196 | 980 |
| 183 and 81 | 4941 |
| 40 and 74 | 1480 |
| 102 and 160 | 8160 |
| 135 and 141 | 6345 |