Least Common Multiple (LCM) of 113 and 97
The least common multiple (LCM) of 113 and 97 is 10961.
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 113 and 97?
First, calculate the GCD of 113 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 97 = 1 remainder 16 |
| 2 | 97 ÷ 16 = 6 remainder 1 |
| 3 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 149 | 6258 |
| 14 and 63 | 126 |
| 161 and 85 | 13685 |
| 35 and 135 | 945 |
| 55 and 164 | 9020 |