Least Common Multiple (LCM) of 178 and 53
The least common multiple (LCM) of 178 and 53 is 9434.
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 178 and 53?
First, calculate the GCD of 178 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 53 = 3 remainder 19 |
| 2 | 53 ÷ 19 = 2 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 96 | 480 |
| 197 and 105 | 20685 |
| 40 and 96 | 480 |
| 127 and 91 | 11557 |
| 31 and 153 | 4743 |