Least Common Multiple (LCM) of 53 and 77
The least common multiple (LCM) of 53 and 77 is 4081.
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 53 and 77?
First, calculate the GCD of 53 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 77 = 0 remainder 53 |
| 2 | 77 ÷ 53 = 1 remainder 24 |
| 3 | 53 ÷ 24 = 2 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 52 | 5460 |
| 51 and 158 | 8058 |
| 188 and 75 | 14100 |
| 56 and 145 | 8120 |
| 164 and 160 | 6560 |