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# Solved Examples(Set 4) - HCF and LCM

 16. A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder? A. 156 B. 211 C. 231 D. 199

Explanation:

If the remainder is same in each case and remainder is not given, HCF of the differences of the numbers is the required largest number.

9997 - 7654 = 2343
9997 - 8506 = 1491
8506 - 7654 = 852

Hence, the greatest number which divides 7654, 8506 and 9997 and leaves same remainder
= HCF of 2343, 1491, 852
= 213

Now we need to find out the common remainder.

Take any of the given numbers from 7654, 8506 and 9997, say 7654

7654 ÷ 213 = 35, remainder = 199

 17. Find the greatest common divisor of 24 and 16 A. 6 B. 8 C. 2 D. 4

Explanation: Hence, greatest common divisor of 24 and 16 = 8

 18. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they again at the starting point ? A. 46 minutes 12 seconds B. 36 minutes 12 seconds C. 36 minutes 22 seconds D. 46 minutes 22 seconds

Explanation:

LCM of 252, 308 and 198 = 2772

Hence they all will be again at the starting point after 2772 seconds.
i.e., after 46 minutes 12 seconds.

 19. The ratio of two numbers is 4 : 5. If the HCF of these numbers is 6, what is their LCM? A. 30 B. 120 C. 60 D. 90

Explanation:

Let the numbers be 4k and 5k

HCF of 4 and 5 = 1
Hence HCF of 4k and 5k = k

Given that HCF of 4k and 5k = 6
=> k = 6

Hence the numbers are (4 × 6) and (5 × 6)
= 24 and 30

LCM of 24 and 30 = 120

 20. What is the HCF of 2.04, 0.24 and 0.8 ? A. 1 B. 0.04 C. 2 D. 0.02

Explanation:

(Refer "How to calculate LCM and HCF of Decimals" here)

Step 1: Make the same number of decimal places in all the given numbers by suffixing zero(s) in required numbers as needed.
=> 2.04, 0.24 and 0.80

Step 2: Now find the HCF of these numbers without decimal.
=> HCF of 204, 24 and 80 = 4

Step 3: Put the decimal point in the result obtained in step 2 leaving as many digits on its right as there are in each of the numbers.
i.e., here we need to put decimal point in the result obtained in step 2 leaving two digits on its right.
=> HCF of 2.04, 0.24 and 0.8 = 0.04