Least Common Multiple (LCM) of 111 and 149
The least common multiple (LCM) of 111 and 149 is 16539.
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 149?
First, calculate the GCD of 111 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 149 = 0 remainder 111 |
| 2 | 149 ÷ 111 = 1 remainder 38 |
| 3 | 111 ÷ 38 = 2 remainder 35 |
| 4 | 38 ÷ 35 = 1 remainder 3 |
| 5 | 35 ÷ 3 = 11 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 123 | 6765 |
| 40 and 113 | 4520 |
| 105 and 22 | 2310 |
| 64 and 45 | 2880 |
| 87 and 24 | 696 |