Least Common Multiple (LCM) of 42 and 76
The least common multiple (LCM) of 42 and 76 is 1596.
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 76?
First, calculate the GCD of 42 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 76 = 0 remainder 42 |
| 2 | 76 ÷ 42 = 1 remainder 34 |
| 3 | 42 ÷ 34 = 1 remainder 8 |
| 4 | 34 ÷ 8 = 4 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 29 | 1624 |
| 69 and 182 | 12558 |
| 160 and 60 | 480 |
| 39 and 157 | 6123 |
| 130 and 71 | 9230 |