Least Common Multiple (LCM) of 46 and 77
The least common multiple (LCM) of 46 and 77 is 3542.
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 46 and 77?
First, calculate the GCD of 46 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 77 = 0 remainder 46 |
| 2 | 77 ÷ 46 = 1 remainder 31 |
| 3 | 46 ÷ 31 = 1 remainder 15 |
| 4 | 31 ÷ 15 = 2 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 30 | 2010 |
| 69 and 18 | 414 |
| 178 and 109 | 19402 |
| 189 and 155 | 29295 |
| 116 and 100 | 2900 |