Least Common Multiple (LCM) of 126 and 27
The least common multiple (LCM) of 126 and 27 is 378.
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 27?
First, calculate the GCD of 126 and 27 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 27 = 4 remainder 18 |
| 2 | 27 ÷ 18 = 1 remainder 9 |
| 3 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 182 | 22386 |
| 149 and 119 | 17731 |
| 10 and 139 | 1390 |
| 165 and 133 | 21945 |
| 166 and 106 | 8798 |