Least Common Multiple (LCM) of 97 and 161
The least common multiple (LCM) of 97 and 161 is 15617.
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 161?
First, calculate the GCD of 97 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 161 = 0 remainder 97 |
| 2 | 161 ÷ 97 = 1 remainder 64 |
| 3 | 97 ÷ 64 = 1 remainder 33 |
| 4 | 64 ÷ 33 = 1 remainder 31 |
| 5 | 33 ÷ 31 = 1 remainder 2 |
| 6 | 31 ÷ 2 = 15 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 99 | 5247 |
| 23 and 56 | 1288 |
| 45 and 93 | 1395 |
| 32 and 172 | 1376 |
| 40 and 56 | 280 |