LCM and HCF
 If the product of three consecutive numbers is 210 then sum of the smaller number is :

View Hint View Answer Discuss in Forum
∴ 210 = 2 × 3 × 5 × 7 = 5 × 6 × 7
Here , 5 and 6 are smaller numbers .Correct Option: D
∴ 210 = 2 × 3 × 5 × 7 = 5 × 6 × 7
Here , 5 and 6 are smaller numbers .
∴ Sum of smaller numbers = 5 + 6 = 11
 The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is

View Hint View Answer Discuss in Forum
We find LCM of 12, 18 , 21 and 32.
∴ LCM of 12, 18 , 21 and 32 = 2 × 2 × 3 × 3 × 7 × 8 = 2016Correct Option: B
We find LCM of 12, 18 , 21 and 32.
∴ LCM of 12, 18 , 21 and 32 = 2 × 2 × 3 × 3 × 7 × 8 = 2016
∴ Required number = 2016 × 2 = 4032
 A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is

View Hint View Answer Discuss in Forum
We find LCM of 30, 36 and 80.
∴ LCM = 2 × 2 × 3 × 3 × 4 × 5 = 720Correct Option: A
We find LCM of 30, 36 and 80.
∴ LCM = 2 × 2 × 3 × 3 × 4 × 5 = 720
∴ Required number = 2 × 720 + 11 = 1440 + 11 = 1451
 The smallest five digit number which is divisible by 12,18 and 21 is :

View Hint View Answer Discuss in Forum
Firstly , we find the LCM of 12, 18 and 21
∴ LCM of 12, 18 and 21 = 2 × 3 × 2 × 3 × 7 = 252Correct Option: C
Firstly , we find the LCM of 12, 18 and 21
∴ LCM of 12, 18 and 21 = 2 × 3 × 2 × 3 × 7 = 252
Of the options, 10080 ÷ 252 = 40
Hence , required answer is 10080 .
 Let p be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of p is

View Hint View Answer Discuss in Forum
We find the LCM of 12 , 16 , 18 and 21
∴ LCM = 2 × 2 × 3 × 4 × 3 × 7 = 1008
2 Multiple of 1008 = 1008 × 2 = 2016
∴ Required number = 2016 – 2000 = 16 = pCorrect Option: A
We find the LCM of 12 , 16 , 18 and 21
∴ LCM = 2 × 2 × 3 × 4 × 3 × 7 = 1008
2 Multiple of 1008 = 1008 × 2 = 2016
∴ Required number = 2016 – 2000 = 16 = p
∴ Sum of digits of p = 1 + 6 = 7