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 |
|---|---|
| 144 and 44 | 1584 |
| 100 and 157 | 15700 |
| 109 and 199 | 21691 |
| 178 and 186 | 16554 |
| 120 and 145 | 3480 |