Question

if a,b,c are prime numbers , then LCM ( a⁵b²c , a³b⁴c² ) = ​

Answer 1

Definition:

The smallest positive number that is a multiple of two or more numbers. Example: the Least Common Multiple of 3 and 5 is 15. Because 15 is a multiple of 3 and also a multiple of 5 and it is the smallest number like that. 3 and 5 have other common multiples such as 30, 45, etc, but they are all larger than 15

Answer:

LCM of a⁵b²c , a³b⁴c² is a³b²c

Answer 2

Answer:

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Step-by-step explanation:

Answer

Correct option is

C

225

It is given that LCM(p,q)=r

2

t

4

s

2

.

That is, at least one of p and q must have r

2

,t

4

and s

2

in their prime factorizations.

Now, consider the cases for power of r as follows:

Case 1: p contains r

2

then q has r

k

with k=(0,1).

That is, number of ways=2.

Case 2: q contains r

2

then p has r

k

with k=(0,1).

That is, number of ways=2.

Case 3: Both p and q contains r

2

Then, number of ways=1.

Therefore, exponent of r may be chosen in 2+2+1=5 ways.

Similarly, exponent of t may be chosen in 4+4+1=9 ways and exponent of s may be chosen in 2+2+1=5 ways

Thus, the total number of ways is:

5×9×5=225