Least Common Multiple (LCM) of 160 and 97
The least common multiple (LCM) of 160 and 97 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 160 and 97?
First, calculate the GCD of 160 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 97 = 1 remainder 63 |
| 2 | 97 ÷ 63 = 1 remainder 34 |
| 3 | 63 ÷ 34 = 1 remainder 29 |
| 4 | 34 ÷ 29 = 1 remainder 5 |
| 5 | 29 ÷ 5 = 5 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 120 | 1680 |
| 175 and 114 | 19950 |
| 136 and 164 | 5576 |
| 14 and 39 | 546 |
| 105 and 97 | 10185 |