Least Common Multiple (LCM) of 42 and 77
The least common multiple (LCM) of 42 and 77 is 462.
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 77?
First, calculate the GCD of 42 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 77 = 0 remainder 42 |
| 2 | 77 ÷ 42 = 1 remainder 35 |
| 3 | 42 ÷ 35 = 1 remainder 7 |
| 4 | 35 ÷ 7 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 57 | 9006 |
| 199 and 180 | 35820 |
| 123 and 113 | 13899 |
| 112 and 177 | 19824 |
| 117 and 196 | 22932 |