Least Common Multiple (LCM) of 53 and 150
The least common multiple (LCM) of 53 and 150 is 7950.
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 150?
First, calculate the GCD of 53 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 150 = 0 remainder 53 |
| 2 | 150 ÷ 53 = 2 remainder 44 |
| 3 | 53 ÷ 44 = 1 remainder 9 |
| 4 | 44 ÷ 9 = 4 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 79 | 9006 |
| 128 and 107 | 13696 |
| 61 and 128 | 7808 |
| 184 and 151 | 27784 |
| 110 and 14 | 770 |