Least Common Multiple (LCM) of 112 and 121
The least common multiple (LCM) of 112 and 121 is 13552.
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 121?
First, calculate the GCD of 112 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 121 = 0 remainder 112 |
| 2 | 121 ÷ 112 = 1 remainder 9 |
| 3 | 112 ÷ 9 = 12 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 16 | 1712 |
| 74 and 152 | 5624 |
| 166 and 197 | 32702 |
| 20 and 169 | 3380 |
| 85 and 92 | 7820 |