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 |
|---|---|
| 80 and 103 | 8240 |
| 200 and 56 | 1400 |
| 158 and 51 | 8058 |
| 132 and 99 | 396 |
| 173 and 134 | 23182 |