Least Common Multiple (LCM) of 53 and 152
The least common multiple (LCM) of 53 and 152 is 8056.
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 152?
First, calculate the GCD of 53 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 152 = 0 remainder 53 |
| 2 | 152 ÷ 53 = 2 remainder 46 |
| 3 | 53 ÷ 46 = 1 remainder 7 |
| 4 | 46 ÷ 7 = 6 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 142 | 12070 |
| 14 and 108 | 756 |
| 74 and 97 | 7178 |
| 185 and 126 | 23310 |
| 150 and 84 | 2100 |