Question

find the smallest number that is divisible by 30,45,60​

Answer 1

Answer:

Smallest number divisible by 30,45,60 is LCM of these numbers

LCM = 180

Answer 2

Answer:

The smallest number that is divisible by 30,45, 60 can be find by taking LCM of these 3 number , So the  LCM of 30,45,60 is 180.

Step-by-step explanation:

Steps to calculate the LCM:

a). divide all three number with the lowest number(i.e., 2) , all three number are divisible by 2

b). again if the remainder is divisible by 2 so divide it until the remainder become 0.

c). if the remainder is not divisible by 2 (ex. 15) divide it with the another smallest number do it till the remainder become 0.

• 30= 2 x 3 x 5
• 45 = 3² x 5

• 60 = 2² x 3 x 5

gcd(30,45)=3 x5

gcd(45 ,60)= 3 x 5

gcd(30, 60) = 2 x 3 x 5

Therefore LCM can be calculated as follows:-

LCM(30, 45, 60) = [(30 × 45 × 60) × gcd(30, 45, 60)]/[GCD(30, 45) × gcd(45, 60) × gcd(30, 60)]

LCM(30, 45, 60) = (81000 × 15)/(15 × 15 × 30) = 180

⇒LCM(30, 45, 60) = 180

Example :

LCM of 7 and 14: - 14

LCM of 27 and 81 :- 81

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