Least Common Multiple (LCM) of 53 and 149
The least common multiple (LCM) of 53 and 149 is 7897.
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 149?
First, calculate the GCD of 53 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 149 = 0 remainder 53 |
| 2 | 149 ÷ 53 = 2 remainder 43 |
| 3 | 53 ÷ 43 = 1 remainder 10 |
| 4 | 43 ÷ 10 = 4 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 24 | 600 |
| 194 and 123 | 23862 |
| 172 and 170 | 14620 |
| 63 and 10 | 630 |
| 148 and 61 | 9028 |