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E:\Working\Focus_Learning\Math_Genius-6\Open_Files\07_Chapter_5\Chapter_5
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Now 120 999 8
– 960
39
\ Greatest 3-digit number exactly divisible by 120 is 999 – 39 = 960

Facts about HCF and LCM

1. The HCF of two co-primes is 1.

2. The HCF of given numbers is not greater than any of the given numbers.
3. The HCF of given numbers is always a factor of their LCM.
4. The LCM of given numbers is not less than any of the given numbers.

5. The LCM of two co-primes is equal to their product.
6. For any two given numbers A and B, such that A is a factor of B, their HCF = A, and LCM = B.

7. Product of any two numbers = Product of their HCF and LCM.
Example 30: The HCF of two numbers is 12 and LCM is 72. If one of the numbers is 36, find the
other number.
Solution: We know that, 1st number × 2nd number = Product of HCF × LCM

⇒ 36 × 2nd number = 12 × 72
12 72 Quick Check
×
⇒ 2nd number = = 24 1. What is the HCF of 5 and 35?
36
Thus, another number is 24. 2. What is the LCM of 6 and 25?
Practice Time 5F

1. Find the HCF of the following numbers using the prime factorisation method.

(a) 18, 26, 72 (b) 118, 460 (c) 104, 58, 106
2. Write the HCF of the following numbers using the long division method.
(a) 44, 144 (b) 12, 168 (c) 40, 56, 17 (d) 632, 790, 869
3. Find the LCM of the following numbers using the prime factorisation method.

(a) 28, 42 (b) 30, 45 (c) 16, 24, 56
4. Find the lowest common multiple of the following numbers.
(a) 30, 48, 120 (b) 12, 15, 36, 45 (c) 107, 118

5. The traffic lights at three different road crossings change every 48 seconds, 60 seconds and 72
seconds, respectively. If they change simultaneously at 9 a.m., at what time will they change again?

6. What is the side of the largest possible square brick that can be paved on the floor of a room 4 m
96 cm long and 4 m 3 cm broad?
7. Find the least number which when divided by 15, 25 and 30 leaves the remainder 8 in each case.

8. The HCF of two numbers is 55 and their LCM is 7700. If one of the numbers is 275, find the other.
9. In a circular stadium, three athletes—Raman, Veena, and Harish—are preparing for a
400-metre race. They begin by running around a circular track, finishing one lap in 36, 40,
and 48 seconds, respectively. How long will it take them to meet at the starting point?

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