Least Common Multiple (LCM) of 110 and 77
The least common multiple (LCM) of 110 and 77 is 770.
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 110 and 77?
First, calculate the GCD of 110 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 77 = 1 remainder 33 |
| 2 | 77 ÷ 33 = 2 remainder 11 |
| 3 | 33 ÷ 11 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 122 | 8418 |
| 51 and 55 | 2805 |
| 89 and 143 | 12727 |
| 32 and 170 | 2720 |
| 189 and 175 | 4725 |