Least Common Multiple (LCM) of 169 and 126
The least common multiple (LCM) of 169 and 126 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 169 and 126?
First, calculate the GCD of 169 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 126 = 1 remainder 43 |
| 2 | 126 ÷ 43 = 2 remainder 40 |
| 3 | 43 ÷ 40 = 1 remainder 3 |
| 4 | 40 ÷ 3 = 13 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 84 | 420 |
| 67 and 44 | 2948 |
| 41 and 188 | 7708 |
| 125 and 132 | 16500 |
| 44 and 135 | 5940 |