Least Common Multiple (LCM) of 112 and 149
The least common multiple (LCM) of 112 and 149 is 16688.
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 112 and 149?
First, calculate the GCD of 112 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 149 = 0 remainder 112 |
| 2 | 149 ÷ 112 = 1 remainder 37 |
| 3 | 112 ÷ 37 = 3 remainder 1 |
| 4 | 37 ÷ 1 = 37 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 89 | 3560 |
| 120 and 108 | 1080 |
| 179 and 189 | 33831 |
| 101 and 138 | 13938 |
| 155 and 141 | 21855 |