Least Common Multiple (LCM) of 36 and 117
The least common multiple (LCM) of 36 and 117 is 468.
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 117?
First, calculate the GCD of 36 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 117 = 0 remainder 36 |
| 2 | 117 ÷ 36 = 3 remainder 9 |
| 3 | 36 ÷ 9 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 131 | 3013 |
| 156 and 78 | 156 |
| 87 and 119 | 10353 |
| 30 and 20 | 60 |
| 175 and 186 | 32550 |