Question
If 20 times a number is subtracted from the square of the number and then 100 is added to the result, then the result is zero. Find the
L.C.M of the number and 15.
Solution
Let the number be 'x' According to the question, x2 - 20x + 100 = 0 Or, x2 - 10x - 10x + 100 = 0 Or, x(x - 10) - 10(x - 10) = 0 Or, (x - 10)(x - 10) = 0 So, x = 10 L.C.M of 10 and 15 = 30
More HCF and LCM Questions
- LCM of two numbers is 64 times of their HCF. Sum of the HCF and LCM is 975. If the first number is 960. Find the other number?
- Let N be the greatest number that will divide 82, 105, 128 leaving the same remainder in each case. Then sum of the digits in N is:
- The LCM of two numbers is 3600 while their HCF is 60. If one of the numbers is 600, then the other number is:
- Find the difference between sum of digits of LCM and HCF of 24, 36 and 90.
- The HCF and LCM of 2 numbers are 2 and 60 respectively. If one of the numbers is 14 more than the other, find the smaller number.
- The HCF of two numbers is 18 and their LCM is 540. If one of the numbers is 90, find the other number.
- Find the difference between sum of digits of LCM and HCF of 28, 42 and 70.
- Three numbers are in the ratio 5:6:9 respectively. If the HCF of the numbers is 2, then find the LCM of the numbers.
- The least number which when divided by 8, 10, 14, 16, and 20 leaves the same remainder 3 in each case, is:
- The sum of two numbers is 156 and their HCF is 26. Find how many such pairs can be formed.
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