Least Common Multiple (LCM) of 149 and 111
The least common multiple (LCM) of 149 and 111 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 149 and 111?
First, calculate the GCD of 149 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 111 = 1 remainder 38 |
| 2 | 111 ÷ 38 = 2 remainder 35 |
| 3 | 38 ÷ 35 = 1 remainder 3 |
| 4 | 35 ÷ 3 = 11 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 169 | 12168 |
| 69 and 160 | 11040 |
| 101 and 176 | 17776 |
| 98 and 55 | 5390 |
| 50 and 189 | 9450 |