Least Common Multiple (LCM) of 160 and 169
The least common multiple (LCM) of 160 and 169 is 27040.
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 169?
First, calculate the GCD of 160 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 169 = 0 remainder 160 |
| 2 | 169 ÷ 160 = 1 remainder 9 |
| 3 | 160 ÷ 9 = 17 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 115 | 4715 |
| 130 and 159 | 20670 |
| 58 and 55 | 3190 |
| 34 and 109 | 3706 |
| 114 and 192 | 3648 |