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Question
Veena has some beads. She wants to make necklaces with an equal number of beads in each. If she makes necklaces of 16 or 24 or 40 beads, there is no bead left over. What is the least number of beads with her?
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Solution
Veena wants to make necklaces with an equal number of beads in each such there is no bead left over, so the number of beads with her must be in multiples of 16, 24, and 40. Therefore, the least number of beads with her is the LCM of 16, 24, and 40.
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288,...
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264,...
Multiples of 40: 40, 80, 120, 160, 200, 240, 280,...
Common multiples of 16, 24, and 40: 240,...
∴ Least number of beads with Veena = LCM of 16, 24 and 40 = 240
Thus, the least number of beads with Veena is 240.
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