Least Common Multiple (LCM) of 169 and 120
The least common multiple (LCM) of 169 and 120 is 20280.
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 120?
First, calculate the GCD of 169 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 120 = 1 remainder 49 |
| 2 | 120 ÷ 49 = 2 remainder 22 |
| 3 | 49 ÷ 22 = 2 remainder 5 |
| 4 | 22 ÷ 5 = 4 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 107 | 16264 |
| 176 and 26 | 2288 |
| 31 and 186 | 186 |
| 191 and 40 | 7640 |
| 35 and 68 | 2380 |