Least Common Multiple (LCM) of 101 and 112
The least common multiple (LCM) of 101 and 112 is 11312.
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 101 and 112?
First, calculate the GCD of 101 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 112 = 0 remainder 101 |
| 2 | 112 ÷ 101 = 1 remainder 11 |
| 3 | 101 ÷ 11 = 9 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 115 | 4370 |
| 142 and 171 | 24282 |
| 15 and 75 | 75 |
| 122 and 144 | 8784 |
| 54 and 126 | 378 |