Least Common Multiple (LCM) of 112 and 97
The least common multiple (LCM) of 112 and 97 is 10864.
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 97?
First, calculate the GCD of 112 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 97 = 1 remainder 15 |
| 2 | 97 ÷ 15 = 6 remainder 7 |
| 3 | 15 ÷ 7 = 2 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 164 | 6396 |
| 156 and 31 | 4836 |
| 39 and 199 | 7761 |
| 145 and 170 | 4930 |
| 99 and 142 | 14058 |