Least Common Multiple (LCM) of 97 and 61
The least common multiple (LCM) of 97 and 61 is 5917.
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 61?
First, calculate the GCD of 97 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 61 = 1 remainder 36 |
| 2 | 61 ÷ 36 = 1 remainder 25 |
| 3 | 36 ÷ 25 = 1 remainder 11 |
| 4 | 25 ÷ 11 = 2 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 135 | 9990 |
| 180 and 136 | 6120 |
| 49 and 86 | 4214 |
| 40 and 115 | 920 |
| 65 and 163 | 10595 |