IDNLearn.com connects you with a community of knowledgeable individuals ready to help. Get accurate and comprehensive answers to your questions from our community of knowledgeable professionals.
Sagot :
Multiples of 400: 400, 800, 1200, 1600
Multiples of 600: 600, 1200, 1800
So the LCM is 1200
Multiples of 600: 600, 1200, 1800
So the LCM is 1200
Step-by-step explanation:
the LCM (least common multiple) is the product (multiplication) of the longest product strings of the prime factors.
prime factors of a number start with 2 (the smallest prime number). we keep dividing the number (and then the results) by 2 until the division is not delivering a whole number anymore. then we switch to the next higher prime number. and so on, until the result is 1.
prime factors of 400
400 : 2 = 200
200 : 2 = 100
100 : 2 = 50
50 : 2 = 25
25 : 2 no
25 : 3 no
25 : 5 = 5
5 : 5 = 1
the prime factorization of 400 is therefore
2×2×2×2×5×5
prime factors of 600
600 : 2 = 300
300 : 2 = 150
150 : 2 = 75
75 : 2 no
75 : 3 = 25
25 : 3 no
25 : 5 = 5
5 : 5 = 1
the prime factorization of 600 is therefore
2×2×2×3×5×5
the LCM is now the product of the longest multiplication chains for the prime factors :
the longest chain for 2 is
2×2×2×2 in 400
for 3 is
3 in 600
for 5 is
5×5 in 400 and 600
the LCM = 2×2×2×2 × 3 × 5×5 = 1,200.
which is much smaller than the "instinctive" product of 400 and 600 :
400×600 = 240,000
which is of course also a multiple of 400 and 600, but not the smallest one (LCM).
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions deserve accurate answers. Thank you for visiting IDNLearn.com, and see you again for more solutions.
