Least Common Multiple (LCM) of 97 and 113
The least common multiple (LCM) of 97 and 113 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 97 and 113?
First, calculate the GCD of 97 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 113 = 0 remainder 97 |
| 2 | 113 ÷ 97 = 1 remainder 16 |
| 3 | 97 ÷ 16 = 6 remainder 1 |
| 4 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 76 | 2356 |
| 63 and 113 | 7119 |
| 119 and 65 | 7735 |
| 72 and 153 | 1224 |
| 147 and 94 | 13818 |