Least Common Multiple (LCM) of 160 and 119
The least common multiple (LCM) of 160 and 119 is 19040.
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 119?
First, calculate the GCD of 160 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 160 ÷ 119 = 1 remainder 41 |
| 2 | 119 ÷ 41 = 2 remainder 37 |
| 3 | 41 ÷ 37 = 1 remainder 4 |
| 4 | 37 ÷ 4 = 9 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 47 | 8413 |
| 140 and 131 | 18340 |
| 78 and 59 | 4602 |
| 173 and 164 | 28372 |
| 75 and 105 | 525 |