The problem asks for the least number that leaves a remainder of 4 when divided by 5, 6, 8, 9, and 12.
Finding LCM of Divisors
To find this least number, we first need to find the Least Common Multiple (LCM) of the divisors: 5, 6, 8, 9, and 12.
First, find the prime factorization of each divisor:
- $5 = 5$
- $6 = 2 \times 3$
- $8 = 2^3$
- $9 = 3^2$
- $12 = 2^2 \times 3$
The LCM is found by taking the highest power of each prime factor present in the factorizations:
LCM = $2^3 \times 3^2 \times 5$
LCM = $8 \times 9 \times 5$
LCM = $72 \times 5$
LCM = $360$
Determining the Least Number
The question states that the number leaves a remainder of 4 in each case. To find the least such number, we add the remainder to the LCM.
Least Number = LCM + Remainder
Least Number = $360 + 4$
Least Number = $364$
Therefore, the least number that leaves a remainder of 4 when divided by 5, 6, 8, 9, and 12 is 364.
Similar Questions
- The H.C.F. and the L.C.M. of two numbers are 5 and 495, respectively. If one of the numbers is 55, find the other one.
- The HCF of two numbers is 16 and their LCM is 240. If one number is 48, find the other number.
- The sum of two numbers is 132 and their L.C.M. is 630. What are the two numbers?
- The LCM of the numbers 12.8 and 0.004 is:
- Find the least number which is divisible by first ten natural numbers.
- Find the HCF of ($3^{45} - 1$) and ($3^{35} - 1$).
- The HCF and LCM of two numbers are in the ratio of 1: 30 and the difference between the HCF and LCM is 493. Find the product of LCM and HCF.
- HCF of $\frac{1}{3}, \frac{3}{4}, \frac{4}{5}$ and $\frac{5}{6}$ is:
- Which of the following is the greatest number that, when dividing 183, 127 and 211, leaves the same remainder each time?
- If the LCM of $20x^3y^2$ and $10x^4y^4$ is $20x^4y^4$, find the HCF.
Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
