Least Common Multiple (LCM) of 152 and 53
The least common multiple (LCM) of 152 and 53 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 152 and 53?
First, calculate the GCD of 152 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 53 = 2 remainder 46 |
| 2 | 53 ÷ 46 = 1 remainder 7 |
| 3 | 46 ÷ 7 = 6 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 107 | 14659 |
| 108 and 136 | 3672 |
| 162 and 178 | 14418 |
| 154 and 150 | 11550 |
| 144 and 27 | 432 |