Least Common Multiple (LCM) of 112 and 101
The least common multiple (LCM) of 112 and 101 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 112 and 101?
First, calculate the GCD of 112 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 101 = 1 remainder 11 |
| 2 | 101 ÷ 11 = 9 remainder 2 |
| 3 | 11 ÷ 2 = 5 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 119 | 8925 |
| 122 and 19 | 2318 |
| 166 and 61 | 10126 |
| 16 and 57 | 912 |
| 82 and 59 | 4838 |