Least Common Multiple (LCM) of 155 and 112
The least common multiple (LCM) of 155 and 112 is 17360.
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 155 and 112?
First, calculate the GCD of 155 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 112 = 1 remainder 43 |
| 2 | 112 ÷ 43 = 2 remainder 26 |
| 3 | 43 ÷ 26 = 1 remainder 17 |
| 4 | 26 ÷ 17 = 1 remainder 9 |
| 5 | 17 ÷ 9 = 1 remainder 8 |
| 6 | 9 ÷ 8 = 1 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 164 | 10660 |
| 191 and 86 | 16426 |
| 65 and 73 | 4745 |
| 105 and 96 | 3360 |
| 95 and 76 | 380 |