Least Common Multiple (LCM) of 97 and 160
The least common multiple (LCM) of 97 and 160 is 15520.
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 160?
First, calculate the GCD of 97 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 97 ÷ 160 = 0 remainder 97 |
| 2 | 160 ÷ 97 = 1 remainder 63 |
| 3 | 97 ÷ 63 = 1 remainder 34 |
| 4 | 63 ÷ 34 = 1 remainder 29 |
| 5 | 34 ÷ 29 = 1 remainder 5 |
| 6 | 29 ÷ 5 = 5 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 100 | 8900 |
| 176 and 129 | 22704 |
| 96 and 56 | 672 |
| 87 and 114 | 3306 |
| 161 and 57 | 9177 |