Least Common Multiple (LCM) of 36 and 111
The least common multiple (LCM) of 36 and 111 is 1332.
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 111?
First, calculate the GCD of 36 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 111 = 0 remainder 36 |
| 2 | 111 ÷ 36 = 3 remainder 3 |
| 3 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 49 | 9555 |
| 151 and 30 | 4530 |
| 154 and 176 | 1232 |
| 121 and 105 | 12705 |
| 165 and 144 | 7920 |