H.C.F. & L.C.M. of Numbers

Q 1: H.C.F. of 513, 1134 and 1215 is ____________ a. 18 b. 27 c. 33 d. 36 Answer: Option b Explanation: H.C.F by division method Q 2: L.C.M of 12,18,30. a. 180 b. 100 c. 160 d. 80 Answer: Option a Explanation: List down the factors of the given numbers as follows: 12=22x3 18=2x33 30=2x3x5 L.C.M=(chose the highest powers of prime factors)=22x33x5 =180. Q 3: Find the largest number of 4-digits divisible by 12, 15 and 18. a. 9900 b. 9750 c. 9450 d. 9000 Answer: Option a Explanation: Required largest number must be divisible by the L.C.M. of 12, 15 and 18 L.C.M. of 12, 15 and 18 12 = 2 × 2 × 3 15 =5 × 3 18 = 2 × 3 × 3 L.C.M. = 180 Now divide 9999 by 180, we get remainder as 99 The required largest number = (9999 – 99) =9900 Number 9900 is exactly divisible by 180. Q 4: The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one of the numbers is 275, then the other is: A.) 267 B.) 318 C.) 308 D.) 279 Answer: Option c Explanation: Other number is = (11 x 7700/275) = 308. Q 5: The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is: A.) 12 B.) 68 C.) 48 D.) 78 Answer: Option c Explanation: Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4. So, the numbers 12 and 16. L.C.M. of 12 and 16 = 48.

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