Least Common Multiple (LCM) of 53 and 179
The least common multiple (LCM) of 53 and 179 is 9487.
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 179?
First, calculate the GCD of 53 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 179 = 0 remainder 53 |
| 2 | 179 ÷ 53 = 3 remainder 20 |
| 3 | 53 ÷ 20 = 2 remainder 13 |
| 4 | 20 ÷ 13 = 1 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 170 | 7990 |
| 89 and 78 | 6942 |
| 123 and 120 | 4920 |
| 76 and 101 | 7676 |
| 104 and 17 | 1768 |