Page 107 - MathGPT_V1.0_C4

E:\Working\Brother_Education\Preparatory_Stage_Maths-4\Open_Files\Chap-05
\\October 31, 2023 4:43 PM Bharat Arora Proof-3 Reader _________________________ Date: ___________________74

Step 3: Find the smallest common multiple.
Here, 18 is the smallest among all these common multiples.

So, the LCM of 6 and 9 is 18.
Example 5: Find the LCM of 10 and 12 by prime factorisation. 2 10 2 12

Solution: Step 1: Find the prime factorisation of given numbers. 5 2 6

10 = 2 × 5 and 12 = 2 × 2 × 3 3
Step 2: Look at the common prime factors. It is 2 only. Also, look at the
factors which are not common in both. They are 5 and 2, 3.

Step 3: Multiply the common prime factors and uncommon factors. The
product of these factors is the required LCM.

So, the LCM of 10 and 12 = 2 × 5 × 2 × 3 = 60.
Example 6: Find the LCM of 14, 21 and 30 by common division.

Solution: Step 1: Arrange the given numbers in a row.

Step 2: Choose a prime divisor that can divide at least two given numbers.
Write the quotients and the undivided numbers in the next row
just below the numbers as shown alongside.
Here, the smallest prime divisor is 2 which can 2 14, 21, 30

divide 14 and 30 exactly. So, we have: 7, 21, 15
Step 3: Continue the step 2 till any two numbers have a common prime
divisor.

Here, the next prime divisor is 3 which can divide 21 2 14, 21, 30
and 15 exactly. And, then 7 is the common divisor. 3 7, 21, 15

Step 4: Multiply the common divisors and numbers left 7 7, 7, 5
in the last row. This product is the required LCM. 1, 1, 5

Thus, LCM of 14, 21 and 30 = 2 × 3 × 7 × 5 = 210.

Practice time 5e

1. Find the hCF by listing factors.

(a) 6, 10 (b) 8, 12 (c) 9, 15 (d) 16, 20, 28
2. Find the hCF by prime factorisation or common division method.

(a) 16, 24 (b) 18, 30 (c) 21, 35 (d) 10, 25, 40

3. Find the LCM by listing some multiples.
(a) 2, 3 (b) 4, 5 (c) 8, 12 (d) 2, 5, 10

4. Find the LCM by prime factorisation or common division method.
(a) 12, 20 (b) 16, 20 (c) 15, 45 (d) 24, 30, 48

Mathematics-4 105