Least Common Multiple (LCM) of 119 and 30
The least common multiple (LCM) of 119 and 30 is 3570.
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 30?
First, calculate the GCD of 119 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 30 = 3 remainder 29 |
| 2 | 30 ÷ 29 = 1 remainder 1 |
| 3 | 29 ÷ 1 = 29 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 69 | 9660 |
| 78 and 148 | 5772 |
| 38 and 57 | 114 |
| 127 and 160 | 20320 |
| 157 and 165 | 25905 |