Least Common Multiple (LCM) of 156 and 53
The least common multiple (LCM) of 156 and 53 is 8268.
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 156 and 53?
First, calculate the GCD of 156 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 53 = 2 remainder 50 |
| 2 | 53 ÷ 50 = 1 remainder 3 |
| 3 | 50 ÷ 3 = 16 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 69 | 7797 |
| 60 and 21 | 420 |
| 73 and 175 | 12775 |
| 52 and 176 | 2288 |
| 194 and 198 | 19206 |