The conversation between human and AI assistant.
Find the least number when it divides by 7,8,9 gives remainder as 1,2,3 respectively?
How did you arrive at that answer?
To find the least common multiple of 7, 8, and 9, we multiply the highest powers of all prime factors involved. The highest prime factors of 7, 8 and 9 are 7, 2^3 and 3^2 respectively. So, we get LCM as 7 x 2^3 x 3^2 = 168, which gives the remainder 1, 0 and 6, when divided by 7, 8 and 9 respectively. To find the least number that gives the remainder of 1, 2 and 3 when divided by 7, 8, and 9 respectively, we add LCM with 1, 2 and 3, and then we find the number that divides LCM and gives the same remainders. Therefore, we get the least number as 2145.