# Selected Questions Based On "HCF and LCM"

Every year we have some questions based on HCF and LCM in SSC, FCI, CDS and other similar competitive exams, which can be solved easily through simple Mathematical tricks and can help us to fetch good marks. We have collected some good questions for your practice through which you can analyse your preparation level.

S.NO |
Questions |

1. | The LCM of two numbers is 2079 and their HCF is 27. If one of the number is 189, Find the other ? |

2. | What is the greatest number that will exactly divide 96, 528 and 792 ? |

3. | Find the greatest number that will divide 728 and 900. Leaving the reminder 8 and 4 respectively ? |

4. | What is the greatest number that will divide 38, 45 and 52 and leaves as reminders 2, 3 and 4 respectively ? |

5. | Find the least number which is exactly divisible by 72,90 and 120 ? |

6. | Find the greatest number of 4 digit which is divisible by 48, 60 and 64 ? |

7. | What is the smallest number which when increased by 3 is divided by 27, 35, 25 and 21 ? |

8. | What is the least number which when lessened by 5 is divisible by 36, 48, 21 and 28 ? |

9. | Find the least number which when divided by 24,32 and 36 leaves the reminders 19, 27 and 31 respectively ? |

10. | Find the least number which when divided by 2, 3, 4, 5 and 6 leaves in each case a reminder as 1? |

11. | Find the least number which when divided by 12, 21 and 35 will leave in each case the same reminder 6 ? |

12. | Find the greatest number which will divide 410,751 and 1030 so as leaves reminder 7 in each case ? |

13. | Find the greatest number which will divide 16997 and 64892 so as it leaves reminder 2 in each case ? |

14. | Find the greatest 4-digit number which when divided by 12, 18, 21 and 28 leaves a reminder 3 in each case ? |

15. | Find the greatest 3-digit number which when divided by 3, 4, and 5 leaves no reminder ? |

16. | Find the smallest 3-digit number, such that it is exactly divisible by 3, 4, and 5 ? |

17. | The product of two numbers is 396*576 and their LCM is 6336. Find their HCF ? |

18. | What is the greatest number that will exactly divide 312, 351, and 650 ? |

19. | What is the greatest number that will divide 29, 60 and 103 and will leave as reminder 7, 12, and 17 respectively ? |

20. | Find the leats number which is exactly divisible by 15, 55 and 99 ? |

21. | Find the greatest number of six digit which on being divided by 6,7,8,9 and 10 leaves 4,5,6,7 and 8 as reminder respectively ? |

22. | Find the greatest number which is such that when 76, 151 and 226 are divided by it, the reminders are all alike. Find also the common reminder ? |

23. | The greatest number of 4 digit which is divisible by each one of numbers 12, 18, 21 and 28 is ? |

24. | What is the least number that must be subtracted from 1936 so that the reminder when divided by 9,10, 15 will leave in each case the same reminder 7 ? |

25. | Three persons A,B,C run along a circular path 12 km long. They start their race from the same point and at the same time with a speed of 3 km/hr, 7km/hr and 13 km/hr respectively. After what time they will meet again ? |

26. | Five bells begin to toll together and toll respectively at intervals of 6,7,8,9 and 12 seconds. How many time will they toll together in one hour ? |

**Answer Key**

(1) 297 | (2) 24 | (3) 16 | (4) 6 | (5) 360 | (6)9600 | (7)1572 | (8) 1013 | (9) 283 |

(10)61 | (11)426 | (12) 31 | (13)1545 | (14) 9831 | (15) 960 | (16) 120 | (17) 36 | (18) 13 |

(19)24 | (20)495 | (21)997918 | (22)75,1 | (23) 9828 | (24) 39 | (25) 8 | (26)12 hrs |