Question

find LCM of 75 45 60 leaves remainder 4 in each case​

Answer 1

Answer:

No remainder  

ii) The remainder 4 in each case.

Step-by-step explanation:

i)

75=3×5  

2

 

45=3  

2

×5

60=2  

2

×3×5

For the greatest 3 digit number which divides by 75,45 and 60 leaves no remainder,

The number must be a multiple of 2  

2

×3  

2

×5  

2

=900

900 is the greatest 3− digit number that is divisible by 75,45, and 60

(ii)

Step 1 find L.C.M of given number

L.C.M of 75,45 and 60 is 900

step 2. find largest 3 digit number which is divisible by 900

largest 3 digit number which is divisible by 900 is itself 900

step 3 add the remainder to the number

900+4=904

Answer 2

75=3×5275=3×52

45=32×545=32×5

60=22×3×560=22×3×5

LCM (75,45,60)=5^2×3^2×2^2=25×9×4=900

Next number divisible by above three numbers is 1800 ,which is 4 digit

Therefore greatest 3 digit number divisible by all three is 900

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