Least Common Multiple (LCM) of 112 and 155
The least common multiple (LCM) of 112 and 155 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 112 and 155?
First, calculate the GCD of 112 and 155 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 155 = 0 remainder 112 |
| 2 | 155 ÷ 112 = 1 remainder 43 |
| 3 | 112 ÷ 43 = 2 remainder 26 |
| 4 | 43 ÷ 26 = 1 remainder 17 |
| 5 | 26 ÷ 17 = 1 remainder 9 |
| 6 | 17 ÷ 9 = 1 remainder 8 |
| 7 | 9 ÷ 8 = 1 remainder 1 |
| 8 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 140 | 700 |
| 146 and 50 | 3650 |
| 81 and 78 | 2106 |
| 163 and 134 | 21842 |
| 147 and 47 | 6909 |