question_answer

Find the LCM of the following numbers:

(a) 9 and 4

(b) 12 and 5

(c) 6 and 5

(d) 15 and 4

Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

Answer:

2	9,	4
2	9,	2
3	9,	1
3	3,	1
	1,	1

LCM \[=3\times 3\times 2\times 2\]          \[=36\]                                                                                                                               (b)

2	12,	5
2	6,	5
3	3,	5
5	1,	5
	1,	1

LCM \[=5\times 3\times 2\times 2\]          \[=60\]                   (c)

2	6	5
3	3	5
5	1	5
1	1

LCM \[=2\times 3\times 5\]          \[=30\]                                                                                                                                           (d)

2	15	4
2	15	2
3	15	1
5	5	1
	1	1

LCM \[=2\times 2\times 3\times 5\]          \[=60\]                                                                                                                   Here, in each case LCM is multiple of 3.                                                                                          Yes, in each case LCM = The product of two numbers.                                                                     LCM of any pair of numbers is not always multiple of 3.                                                                    For Example/LCM of 4 and 14 is 28, which is not multiple of 3.