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 |
|---|---|
| 159 and 199 | 31641 |
| 123 and 42 | 1722 |
| 95 and 33 | 3135 |
| 41 and 176 | 7216 |
| 129 and 117 | 5031 |