Least Common Multiple (LCM) of 160 and 75
The least common multiple (LCM) of 160 and 75 is 2400.
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 75?
First, calculate the GCD of 160 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 75 = 2 remainder 10 |
| 2 | 75 ÷ 10 = 7 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 25 | 2725 |
| 154 and 141 | 21714 |
| 114 and 82 | 4674 |
| 154 and 42 | 462 |
| 149 and 195 | 29055 |