Least Common Multiple (LCM) of 111 and 156
The least common multiple (LCM) of 111 and 156 is 5772.
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 111 and 156?
First, calculate the GCD of 111 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 156 = 0 remainder 111 |
| 2 | 156 ÷ 111 = 1 remainder 45 |
| 3 | 111 ÷ 45 = 2 remainder 21 |
| 4 | 45 ÷ 21 = 2 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 123 | 8733 |
| 54 and 84 | 756 |
| 118 and 72 | 4248 |
| 78 and 53 | 4134 |
| 30 and 178 | 2670 |