What is the GCD for 1715 and 1225?
What is the LCM for 1715 and 1225?
1715 = 49*35 = 7*7*35
1225 = 35*35 = 7*5*35
The Greatest Common Divisor is 7*35 = 245
The Least Common Multiple is
245*7*5 = 8575
To find the greatest common divisor (GCD) of two numbers, such as 1715 and 1225, you can use the Euclidean algorithm. The algorithm involves dividing the larger number by the smaller number and then taking the remainder. This process is repeated until the remainder is zero. The last non-zero remainder is the GCD.
Let's calculate the GCD step by step:
1. Divide 1715 by 1225: 1715 ÷ 1225 = 1 with a remainder of 490.
2. Divide 1225 by the remainder (490): 1225 ÷ 490 = 2 with a remainder of 245.
3. Divide the previous remainder (490) by the new remainder (245): 490 ÷ 245 = 2 with a remainder of 0.
Since the remainder is now zero, we stop. The GCD of 1715 and 1225 is the last non-zero remainder, which is 245.
Now, let's calculate the least common multiple (LCM) of 1715 and 1225. The LCM is the smallest positive integer that is divisible by both numbers.
To find the LCM, you can use the formula:
LCM(a, b) = (a * b) / GCD(a, b)
Using this formula, we can calculate the LCM as follows:
LCM(1715, 1225) = (1715 * 1225) / 245 = 847375 / 245 = 3463.
Therefore, the GCD for 1715 and 1225 is 245, and the LCM is 3463.