Least Common Multiple (LCM) of 180 and 97
The least common multiple (LCM) of 180 and 97 is 17460.
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 180 and 97?
First, calculate the GCD of 180 and 97 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 97 = 1 remainder 83 |
| 2 | 97 ÷ 83 = 1 remainder 14 |
| 3 | 83 ÷ 14 = 5 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 92 | 6164 |
| 153 and 23 | 3519 |
| 123 and 188 | 23124 |
| 127 and 128 | 16256 |
| 42 and 182 | 546 |