Least Common Multiple (LCM) of 61 and 97
The least common multiple (LCM) of 61 and 97 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 61 and 97?
First, calculate the GCD of 61 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 97 = 0 remainder 61 |
| 2 | 97 ÷ 61 = 1 remainder 36 |
| 3 | 61 ÷ 36 = 1 remainder 25 |
| 4 | 36 ÷ 25 = 1 remainder 11 |
| 5 | 25 ÷ 11 = 2 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 189 | 19467 |
| 68 and 98 | 3332 |
| 130 and 63 | 8190 |
| 161 and 72 | 11592 |
| 29 and 108 | 3132 |