Least Common Multiple (LCM) of 102 and 53
The least common multiple (LCM) of 102 and 53 is 5406.
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 102 and 53?
First, calculate the GCD of 102 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 53 = 1 remainder 49 |
| 2 | 53 ÷ 49 = 1 remainder 4 |
| 3 | 49 ÷ 4 = 12 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 51 | 3315 |
| 15 and 29 | 435 |
| 124 and 144 | 4464 |
| 182 and 179 | 32578 |
| 167 and 162 | 27054 |