Least Common Multiple (LCM) of 42 and 68
The least common multiple (LCM) of 42 and 68 is 1428.
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 42 and 68?
First, calculate the GCD of 42 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 68 = 0 remainder 42 |
| 2 | 68 ÷ 42 = 1 remainder 26 |
| 3 | 42 ÷ 26 = 1 remainder 16 |
| 4 | 26 ÷ 16 = 1 remainder 10 |
| 5 | 16 ÷ 10 = 1 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 196 | 3136 |
| 179 and 56 | 10024 |
| 137 and 120 | 16440 |
| 51 and 190 | 9690 |
| 196 and 189 | 5292 |