Least Common Multiple (LCM) of 119 and 42
The least common multiple (LCM) of 119 and 42 is 714.
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 42?
First, calculate the GCD of 119 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 42 = 2 remainder 35 |
| 2 | 42 ÷ 35 = 1 remainder 7 |
| 3 | 35 ÷ 7 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 135 | 2970 |
| 114 and 75 | 2850 |
| 15 and 155 | 465 |
| 39 and 41 | 1599 |
| 20 and 90 | 180 |