Least Common Multiple (LCM) of 162 and 77
The least common multiple (LCM) of 162 and 77 is 12474.
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 162 and 77?
First, calculate the GCD of 162 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 77 = 2 remainder 8 |
| 2 | 77 ÷ 8 = 9 remainder 5 |
| 3 | 8 ÷ 5 = 1 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 121 | 12705 |
| 199 and 58 | 11542 |
| 171 and 167 | 28557 |
| 184 and 73 | 13432 |
| 38 and 60 | 1140 |