Least Common Multiple (LCM) of 135 and 21
The least common multiple (LCM) of 135 and 21 is 945.
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 135 and 21?
First, calculate the GCD of 135 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 21 = 6 remainder 9 |
| 2 | 21 ÷ 9 = 2 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 31 | 4278 |
| 90 and 192 | 2880 |
| 146 and 50 | 3650 |
| 68 and 162 | 5508 |
| 180 and 127 | 22860 |