Least Common Multiple (LCM) of 119 and 32
The least common multiple (LCM) of 119 and 32 is 3808.
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 32?
First, calculate the GCD of 119 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 32 = 3 remainder 23 |
| 2 | 32 ÷ 23 = 1 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 163 | 29666 |
| 14 and 59 | 826 |
| 96 and 130 | 6240 |
| 83 and 142 | 11786 |
| 182 and 114 | 10374 |