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 |
|---|---|
| 102 and 153 | 306 |
| 71 and 192 | 13632 |
| 36 and 108 | 108 |
| 57 and 141 | 2679 |
| 61 and 64 | 3904 |