Least Common Multiple (LCM) of 126 and 168
The least common multiple (LCM) of 126 and 168 is 504.
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 168?
First, calculate the GCD of 126 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 168 = 0 remainder 126 |
| 2 | 168 ÷ 126 = 1 remainder 42 |
| 3 | 126 ÷ 42 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 117 | 12402 |
| 69 and 146 | 10074 |
| 132 and 184 | 6072 |
| 24 and 100 | 600 |
| 52 and 109 | 5668 |