Least Common Multiple (LCM) of 119 and 160
The least common multiple (LCM) of 119 and 160 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 119 and 160?
First, calculate the GCD of 119 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 160 = 0 remainder 119 |
| 2 | 160 ÷ 119 = 1 remainder 41 |
| 3 | 119 ÷ 41 = 2 remainder 37 |
| 4 | 41 ÷ 37 = 1 remainder 4 |
| 5 | 37 ÷ 4 = 9 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 38 | 798 |
| 185 and 113 | 20905 |
| 59 and 128 | 7552 |
| 21 and 192 | 1344 |
| 48 and 43 | 2064 |