Least Common Multiple (LCM) of 34 and 42
The least common multiple (LCM) of 34 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 34 and 42?
First, calculate the GCD of 34 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 42 = 0 remainder 34 |
| 2 | 42 ÷ 34 = 1 remainder 8 |
| 3 | 34 ÷ 8 = 4 remainder 2 |
| 4 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 86 | 9546 |
| 181 and 99 | 17919 |
| 187 and 81 | 15147 |
| 29 and 69 | 2001 |
| 189 and 180 | 3780 |