The least common multiple of 345, 453, 234 is ________.

Question

Accepted Answer

{"content":[{"content":[{"text":"Step 1 (Find Prime Factorization of each number):","type":"text","marks":[{"type":"bold"}]},{"type":"text","text":" We factorize the three numbers:"}],"type":"paragraph"},{"type":"ordered_list","attrs":{"start":1},"content":[{"type":"list_item","content":[{"content":[{"attrs":{"latex":"345 = 3 \times 115 = 3 \times 5 \times 23"},"type":"math_inline"}],"type":"paragraph"}]},{"content":[{"content":[{"attrs":{"latex":"453 = 3 \times 151"},"type":"math_inline"},{"text":" (since 151 is prime)","type":"text"}],"type":"paragraph"}],"type":"list_item"},{"type":"list_item","content":[{"content":[{"attrs":{"latex":"234 = 2 \times 117 = 2 \times 3^2 \times 13"},"type":"math_inline"}],"type":"paragraph"}]}]},{"content":[{"text":"Step 2 (Form the LCM):","type":"text","marks":[{"type":"bold"}]},{"text":" The LCM is formed by taking the highest exponent of each unique prime appearing in these factorizations:","type":"text"}],"type":"paragraph"},{"type":"bullet_list","content":[{"content":[{"content":[{"text":"Prime 2: ","type":"text"},{"attrs":{"latex":"2^1"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"},{"type":"list_item","content":[{"content":[{"type":"text","text":"Prime 3: "},{"attrs":{"latex":"3^2"},"type":"math_inline"}],"type":"paragraph"}]},{"type":"list_item","content":[{"type":"paragraph","content":[{"text":"Prime 5: ","type":"text"},{"attrs":{"latex":"5^1"},"type":"math_inline"}]}]},{"content":[{"content":[{"text":"Prime 13: ","type":"text"},{"attrs":{"latex":"13^1"},"type":"math_inline"}],"type":"paragraph"}],"type":"list_item"},{"type":"list_item","content":[{"type":"paragraph","content":[{"type":"text","text":"Prime 23: "},{"attrs":{"latex":"23^1"},"type":"math_inline"}]}]},{"type":"list_item","content":[{"content":[{"text":"Prime 151: ","type":"text"},{"attrs":{"latex":"151^1"},"type":"math_inline"}],"type":"paragraph"}]}]},{"attrs":{"latex":"\text{LCM} = 2^1 \times 3^2 \times 5^1 \times 13^1 \times 23^1 \times 151^1"},"type":"math_block"},{"attrs":{"latex":"\text{LCM} = 90 \times 13 \times 23 \times 151"},"type":"math_block"},{"attrs":{"latex":"\text{LCM} = 1170 \times 23 \times 151 = 26910 \times 151"},"type":"math_block"},{"attrs":{"latex":"\text{LCM} = 4063410"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"text":" The Least Common Multiple of the three numbers is exactly ","type":"text"},{"marks":[{"type":"code"}],"text":"4063410","type":"text"},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

Guide / Hint

Solution