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Q.

Find the smallest and largest four-digit numbers which when lessened by 12 are exactly divisible by  https://lh5.googleusercontent.com/xACIeFojeX4yxU0tBkMaoCDs6HdPHu6NlS_1n8i7a878UrD1_S12BePN1Qf3NNES7FfJXde4EdHpqzcBgwV3bT7qNNzZA3Hx6JVtDU_UL4_ikh9Bf3znfCd1dd8Eq9WGFmagmGi0ujZr9HBrVa_mnQ


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a

https://lh4.googleusercontent.com/yPUlfxyG9MQcYn27CZngE9_ZM9nQkC5ChKA4049562gdwUKwIH7rj7v5Zi37gWO1itnMmaooPC4ZJ64Y44LyRJ5Ztz8nNQD1tVA5tufrTwK6Rc1pKuAAnLmIU5pluGZVFt5qAIHGSKXxQkTraj3_qg

b

https://lh4.googleusercontent.com/Rl5SRFtCHdo6Y-oO7EzZ3QWV4r67yK_WZ9zzpfJ8t4LQSKk8MEdlrOyYbwhP72XTMSCu2VdnY-okLRcszWsIteCFULMy7WRGF7cTumv9F0wjPLOUDb94tj4nGGzPaDSkPEKPEwi8wcqtyFBw6WjrCw

c

https://lh3.googleusercontent.com/_aUVCAxfTZlOVIY4uR93OGfL_f7EpEjvYlawDCiWmyg4G19ZTtn7-YntivJztsPvmm2fMS9QkcYaiV5Lc7dVUG5OyF6gwKN2zBziXW4M7ZvJ_dIJZz62k7StDeKG6vnlsnNLCoZHcimoWidfXK1chQ

d

https://lh4.googleusercontent.com/sRzOmS9rGYJkUlNgPX5tfSlABtmUMr0oVDXSBL5mXq8q_SQzAQ46mD--B1SP9gx8yToG_vZjjUwT0P7YPyuyjgfW434qiP4PcVzXfTv-veK7wO9yDZ1Rgfh01BDDdah84vcdrGDNZ8l8vhaBEqS7qQ

answer is C.

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Detailed Solution

Concept- In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple. The smallest number among all the common multiples of the provided numbers is the least common multiple of two or more numbers. Consider the integers 2 and 5. There will be different multiples for each.
We can easily find the L.C.M of given integers simply by using the prime factorization method.
The smallest number is https://lh4.googleusercontent.com/e2jXKcoL5FSgQZdXB1RKdAzgXcQ5RMRJTLN7E4ml6pKuROhxsr8qepYxayxZcRAaSCpGl9d2XZfiYqPq6SmWdbIBRauQyli-HiDvANQHUfa0W6ouPlI2OTCO7yk4kyYE2fn-V24vA4eZxqmF94HPIQ  that completely divides the numbers https://lh6.googleusercontent.com/uq4C94ivWvLAHf_p2vtpnP-QuirVW4G5Yg8oBunVKgl9R3lO6ZDSXIdfwDqYwNgEw413J1uNbU3MIM_XMF2BBPqOjOx-RzVnNbwuB3Q5sgoPb5yn7zxykZ59st5NhW4zJ59NOOi9JO4klgm2jJC1HASo, our required number is https://lh3.googleusercontent.com/br252yvxWBGTzI7eRt6Evc5LUgDtudth5eC3J-bFK9ZA8VKxygTFAbawRHMZ49FqDUVz3yROmRqgWVY56Eht_a5MGqDOYuJiipQkx3FiHHq7jTNh8lbPUiIFk-WGKLWl0OnnfYK6-pyeZZBQoE7JtgThe greatest number is https://lh3.googleusercontent.com/C2saehhUGxVNHaRZCI-45d5eRpaBF0G9-U8J4cHjeBKfirRL2Tk6h0rihQFkB6QiDZwnePTFG7lwpa3rqhDmN7kAqUNGV1x_ieIsi52h3CXNaQjuaT3DzZb3DQk5QjEhSqEMftkW-HoNcGCfEQFyyQ that  completely divides the numbers https://lh3.googleusercontent.com/glSJgAu9QOgoG3COarPLCULdsuZ7nngO5NWfeS64xQ7x1eFYLfjjOlQi904K7BN2ZtLeawg0rDiDo_eoWUc8YSXi1jlsuj_peUHPJ_81bvccxAh2UCHkHyXfl7PAOWnuq6AwgCOu8oJGeqdu4Plb4wSo, our required number is https://lh6.googleusercontent.com/AySxMlvWT45mTsnr6OspNXXCzRF1e-UCq326urJUiQQh50BsgLvsqwIlahmXnPa0s5DBkvnT3wN5FkPhHz0_4QFtE1IT6v8-Nu4q7OwMLEhVHO_93MOZmtof3kmJAFG5d5EOzxkTQdXXzwylYz8jcgHence, the correct answer is option number 3) https://lh3.googleusercontent.com/_aUVCAxfTZlOVIY4uR93OGfL_f7EpEjvYlawDCiWmyg4G19ZTtn7-YntivJztsPvmm2fMS9QkcYaiV5Lc7dVUG5OyF6gwKN2zBziXW4M7ZvJ_dIJZz62k7StDeKG6vnlsnNLCoZHcimoWidfXK1chQ 
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Find the smallest and largest four-digit numbers which when lessened by 12 are exactly divisible by