Least Common Multiple (LCM) of 169 and 180
The least common multiple (LCM) of 169 and 180 is 30420.
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 169 and 180?
First, calculate the GCD of 169 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 180 = 0 remainder 169 |
| 2 | 180 ÷ 169 = 1 remainder 11 |
| 3 | 169 ÷ 11 = 15 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 112 | 5936 |
| 41 and 44 | 1804 |
| 172 and 102 | 8772 |
| 30 and 147 | 1470 |
| 14 and 48 | 336 |