lcm(2, 3, 5) = 30 → 2 digit common multiples are 30, 60, 90.
5,3,4, and 2 have many common denominators. What is the least common denominator of all of them?Let's look at the multiples of each number. We do this because common denominators are really common multiples of the denominators. And the LCD is really just the least common multiple (LCM) of the denominators.Starting with 2, the 3, and 4 and last 5 we have the following lists of multiples:2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,68,603,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,604,8,12,16,20,24,28,32,36,40,44,48,52, 56,605,10,15,20,25,30,35,40,45,50,55,60So 60 is the first common multiple and it is the least common denominator of 2, 3, 4 and 5. Note that we could also factor 2, 3, 4 and 5 into primes (2, 3 and 5 already are) So we have 2, 3, 2^2 and 5 We take the largest exponent possible from each and we have 3 x 2^2 x 5 = 20 x 3 = 60. This is the faster way to do this.
30 is divisible by, and is the least common multiple of, 2, 3, and 5.
60 (15 = 3*5, 12=2*2*3 -> 2*2*3*5 = 60)
15
The prime factors of 600 are 2, 2, 2, 3, 5, and 5. The prime factors of 1350 are 2, 3, 3, 3, 5, and 5. The prime factors they have in common are 2, 3, 5, and 5, so the greatest common factor is 2 x 3 x 5 x 5 = 150.
The prime factors of 720 are 2, 2, 2, 2, 3, 3, and 5. The prime factors of 450 are 2, 3, 3, 5, and 5. The prime factors they have in common are 2, 3, 3, and 5, so the greatest common factor is 2 x 3 x 3 x 5 = 90.
The least common multiple of 3 , 2 , 5 = 30
The Least Common Multiple (LCM) for 2 3 5 is 30.
The Least Common Multiple (LCM) for 2 5 3 is 30.
240 = 2*2*2*2*3*5 450 = 2*3*3*5*5 We take all the prime factors they have in common and multiply. This gives 2*3*5 = 30.
lcm(2, 3, 5) = 30 → 2 digit common multiples are 30, 60, 90.
5,3,4, and 2 have many common denominators. What is the least common denominator of all of them?Let's look at the multiples of each number. We do this because common denominators are really common multiples of the denominators. And the LCD is really just the least common multiple (LCM) of the denominators.Starting with 2, the 3, and 4 and last 5 we have the following lists of multiples:2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,68,603,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,604,8,12,16,20,24,28,32,36,40,44,48,52, 56,605,10,15,20,25,30,35,40,45,50,55,60So 60 is the first common multiple and it is the least common denominator of 2, 3, 4 and 5. Note that we could also factor 2, 3, 4 and 5 into primes (2, 3 and 5 already are) So we have 2, 3, 2^2 and 5 We take the largest exponent possible from each and we have 3 x 2^2 x 5 = 20 x 3 = 60. This is the faster way to do this.
3 To clarify: The prime factors of 45 are 3, 3, and 5 (or 32, 5.) The prime factors of 60 are 2, 2, 3, and 5 (or 22, 3, 5.) Therefore, the common factors are 1, 3, 5, and 15, while the common prime factors are only 3 and 5.
The prime factors of 70 are 2, 5, and 7. The prime factors of 90 are 2, 3, 3, and 5. The prime factors that 70 and 90 have in common are 2 and 5. The greatest common factor of 70 and 90 is the product of the prime factors they have in common, so it is 2 x 5 = 10.
The least common multiple of 3 and 5 is 15. This, however is not a multiple of 2 so we must find the next common multiple of 3 and 5. This is 30. Since 30 is also a multiple of 2, 30 is therefore the least common multiple of 3, 5 and 2.
All are primes, so their LCM will be their product. 2 x 3 x 5 = 30.