gcd and lcm of three numbers are 3 and 1008 respectively.if the twi numbers are 48 and 72 find the least possible number
Answers
Answer:
Well, the LCM is 2520=40*63=2^3*3^2*5*7, while the GCM is 6=2*3. The two given numbers are 72=2^3*3^2 and 180=2^2*3^2*5. The LCM of these two numbers is 2^3*3^2*5, so the only factor missing from the given LCM is 7. So the number we seek must have 7 as a factor. It must be divisible by 6 as well, so the least number that does the job is 6*7=42.
Answer: 21
Step-by-step explanation:
In mathematics, the value that is equally divided by the two supplied numbers is known as the LCM of any two. Least Common Multiple is its full name. Another name for it is the Least Common Divisor (LCD). As an illustration, LCM (4, 5) = 20. In this case, the LCM 20 may be divided by both 4 and 5, hence these two numbers are referred to as the divisors of 20.
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since 15 and 10 can both be split by 5, 5 is the biggest common factor between both.
The factors of 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7
The factors of 3 = 3
The factors of 48 = 2 x 2 x 2 x 2 x 3
The factors of 72 = 2 x 2 x 2 x 3 x 3
For the LCM to be 1008, 7 must be included
For the GCD to be 3, 3 also must be included
Therefore, the number is equal to 3 x 7 = 21
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