Least Common Multiple (LCM) of 112 and 171
The least common multiple (LCM) of 112 and 171 is 19152.
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 171?
First, calculate the GCD of 112 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 171 = 0 remainder 112 |
| 2 | 171 ÷ 112 = 1 remainder 59 |
| 3 | 112 ÷ 59 = 1 remainder 53 |
| 4 | 59 ÷ 53 = 1 remainder 6 |
| 5 | 53 ÷ 6 = 8 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 115 | 19435 |
| 69 and 15 | 345 |
| 87 and 31 | 2697 |
| 180 and 152 | 6840 |
| 59 and 198 | 11682 |