Least Common Multiple (LCM) of 45 and 119
The least common multiple (LCM) of 45 and 119 is 5355.
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 45 and 119?
First, calculate the GCD of 45 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 119 = 0 remainder 45 |
| 2 | 119 ÷ 45 = 2 remainder 29 |
| 3 | 45 ÷ 29 = 1 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 120 | 1560 |
| 37 and 46 | 1702 |
| 53 and 82 | 4346 |
| 25 and 64 | 1600 |
| 187 and 64 | 11968 |