Least Common Multiple (LCM) of 80 and 42
The least common multiple (LCM) of 80 and 42 is 1680.
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 80 and 42?
First, calculate the GCD of 80 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 42 = 1 remainder 38 |
| 2 | 42 ÷ 38 = 1 remainder 4 |
| 3 | 38 ÷ 4 = 9 remainder 2 |
| 4 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 129 | 6579 |
| 136 and 194 | 13192 |
| 120 and 64 | 960 |
| 74 and 37 | 74 |
| 120 and 121 | 14520 |