Least Common Multiple (LCM) of 53 and 178
The least common multiple (LCM) of 53 and 178 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 53 and 178?
First, calculate the GCD of 53 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 178 = 0 remainder 53 |
| 2 | 178 ÷ 53 = 3 remainder 19 |
| 3 | 53 ÷ 19 = 2 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 64 | 6720 |
| 139 and 132 | 18348 |
| 145 and 86 | 12470 |
| 42 and 91 | 546 |
| 156 and 14 | 1092 |