Least Common Multiple (LCM) of 77 and 120
The least common multiple (LCM) of 77 and 120 is 9240.
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 77 and 120?
First, calculate the GCD of 77 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 120 = 0 remainder 77 |
| 2 | 120 ÷ 77 = 1 remainder 43 |
| 3 | 77 ÷ 43 = 1 remainder 34 |
| 4 | 43 ÷ 34 = 1 remainder 9 |
| 5 | 34 ÷ 9 = 3 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 33 | 2805 |
| 134 and 67 | 134 |
| 98 and 96 | 4704 |
| 193 and 113 | 21809 |
| 138 and 26 | 1794 |