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 |
|---|---|
| 32 and 40 | 160 |
| 98 and 199 | 19502 |
| 171 and 172 | 29412 |
| 57 and 162 | 3078 |
| 49 and 81 | 3969 |