Least Common Multiple (LCM) of 192 and 53
The least common multiple (LCM) of 192 and 53 is 10176.
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 192 and 53?
First, calculate the GCD of 192 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 192 ÷ 53 = 3 remainder 33 |
| 2 | 53 ÷ 33 = 1 remainder 20 |
| 3 | 33 ÷ 20 = 1 remainder 13 |
| 4 | 20 ÷ 13 = 1 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 157 | 14444 |
| 52 and 159 | 8268 |
| 35 and 98 | 490 |
| 146 and 113 | 16498 |
| 132 and 160 | 5280 |