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 |
|---|---|
| 138 and 141 | 6486 |
| 175 and 178 | 31150 |
| 105 and 44 | 4620 |
| 131 and 62 | 8122 |
| 162 and 86 | 6966 |