Least Common Multiple (LCM) of 30 and 77
The least common multiple (LCM) of 30 and 77 is 2310.
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 30 and 77?
First, calculate the GCD of 30 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 77 = 0 remainder 30 |
| 2 | 77 ÷ 30 = 2 remainder 17 |
| 3 | 30 ÷ 17 = 1 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 122 | 14518 |
| 68 and 166 | 5644 |
| 105 and 93 | 3255 |
| 178 and 113 | 20114 |
| 24 and 64 | 192 |