Least Common Multiple (LCM) of 53 and 156
The least common multiple (LCM) of 53 and 156 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 53 and 156?
First, calculate the GCD of 53 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 156 = 0 remainder 53 |
| 2 | 156 ÷ 53 = 2 remainder 50 |
| 3 | 53 ÷ 50 = 1 remainder 3 |
| 4 | 50 ÷ 3 = 16 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 79 | 12640 |
| 124 and 193 | 23932 |
| 189 and 14 | 378 |
| 20 and 56 | 280 |
| 140 and 21 | 420 |