Least Common Multiple (LCM) of 160 and 175
The least common multiple (LCM) of 160 and 175 is 5600.
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 175?
First, calculate the GCD of 160 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 175 = 0 remainder 160 |
| 2 | 175 ÷ 160 = 1 remainder 15 |
| 3 | 160 ÷ 15 = 10 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 15 | 345 |
| 71 and 145 | 10295 |
| 149 and 188 | 28012 |
| 136 and 75 | 10200 |
| 73 and 13 | 949 |