Least Common Multiple (LCM) of 36 and 54
The least common multiple (LCM) of 36 and 54 is 108.
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 36 and 54?
First, calculate the GCD of 36 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 54 = 0 remainder 36 |
| 2 | 54 ÷ 36 = 1 remainder 18 |
| 3 | 36 ÷ 18 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 198 | 16236 |
| 74 and 12 | 444 |
| 112 and 144 | 1008 |
| 179 and 114 | 20406 |
| 141 and 46 | 6486 |