Least Common Multiple (LCM) of 76 and 55
The least common multiple (LCM) of 76 and 55 is 4180.
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 76 and 55?
First, calculate the GCD of 76 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 55 = 1 remainder 21 |
| 2 | 55 ÷ 21 = 2 remainder 13 |
| 3 | 21 ÷ 13 = 1 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 85 | 12495 |
| 64 and 136 | 1088 |
| 148 and 109 | 16132 |
| 182 and 135 | 24570 |
| 147 and 180 | 8820 |